Leaving a gentile alone in one’s home:
It is initially forbidden to allow a gentile to remain alone with one’s eating utensils/vessels due to worry that he may use the vessels to cook non-Kosher foods [either non-Kosher ingredients or meat with milk]. This applies even if one plans to not use the vessels again until after 24 hours. This applies whether one desires to leave a vessel in the house of a gentile, or desires to leave a gentile alone in his home.
Yotzei Venichnas: If one is coming in and out of the house constantly then it is permitted to leave the gentile alone in one’s home even initially.
Leaving gentile at home while food is cooking: One is to be stringent not to leave pots [of cooking food] with one’s gentile maid when there are no Jews at home. If however, one is constantly coming in and out of the house than one may do so. If however, the maid knows that one will be gone for quite some time, such as he will be leaving to go to Shul and the like, one should be stringent.
Within 24 hours: If one transgressed and left a gentile alone with his vessels then he may not use his vessels [with hot foods] until the passing of slightly more than 24 hours from when the vessel was first left by the gentile. If one transgressed and cooked food in the vessel within 24 hours, the food is forbidden. Some Poskim however are lenient in a time of need, while others forbid the food in all cases.
After 24 hours: After slightly more than 24 hours have passed [since it was first left alone with the gentile], the vessels may be used as usual [even with Davar Charif]. Certainly, it may be used after 24 hours have passed since he retrieved the vessel from the gentile. Some Poskim however rule that if one left the vessels with the gentile Bemeizid then the vessels are forbidden even after 24 hours and either must be Kashered [i.e. metal] or broken [i.e. earthenware]. If, however the vessels were left with the gentile by mistake then one may be lenient after 24 hours if the vessel is not Kasherable, while if it is Kasherable it is to be Kashered. [Practically, if one left the vessels with the gentile Beshogeig and 24 hours passed since one retrieved the vessels, one may be lenient to use them without Kashering.]
Vessels not commonly used for hot foods and law of cups: The above requirement to wait 24 hours only applies to vessels that are commonly eaten with hot foods [of a Keli Rishon or vessels that are used to drink wine]. However, those vessels that are not commonly used with hot foods [of a Keli Rishon, and are not used to drink wine] may be used even within the 24 hours, so long as they are properly washed. [Accordingly, only pots, pans and servicing spoons that are commonly used with a Keli Rishon or Iruiy Keli Rishon must be delayed 24 hours prior to use. However, forks, spoons and knives and the like that are only commonly used for a Keli Sheiyni, or for cold, may be used even right away. Cups, being that they may have been used with wine, must be Kashered even after the passing of 24 hours.]
Leaving the vessel by the gentile for short amount of time: The above only applies if the vessels remained in the home with the gentile for a considerable amount of time, such as half a day, however if it remained there for a mere hour, the vessels may be used as usual.
May one leave eating utensils alone with a non-religious Jew?
 Michaber/Rama Y.D. 122/9; Mordechai Perek Ein Mamidim, quoted in Taz 122/8
 Igros Moshe Y.D. 3/61
 Michaber ibid; Mordechai ibid
 Rama ibid; Shach 122/8; Taz 122/8
 Michaber Y.D. 122/9 regarding bringing to house of gentile; Rama ibid that the same applies to leaving a gentile in one’s home.
 Shach 122/9 that so is custom today being that one may even initially rely on Yotzei Venichnas; Rama 118/12 brought next
 Michaber 118/12; Tur in name of Rosh Kelal 19/18; Vetzrauch Iyun why the Poskim here make no mention of the discussion of Bedieved in 122/9; Perhaps one can say there is a difference between one’s maid working in one’s house [the case here] which we are always lenient Bedieved and a case where one sends his item to the gentile’s house [the case in 122]. Vetzaruch Iyun. See coming footnotes in Bedieved.
The reason: As she may enter into it non-Kosher food. [Shach 118/37]
 Rama ibid
 Shach 118/37 in conclusion of opinion of Rama in ur and Rosh ibid
 Rama ibid
Other opinions: Some Poskim rule that the entire issue of not leaving one’s vessel entrusted with a gentile is only initially, while Bedieved, it may be used at all times. [Implication of Michaber 118/12 and 122/9 who simply writes “Yeish Lehachmir and Yeish Lizaher” and so learns Aruch Hashulchan 122/18 in Michaber] The reason for this is because “Lo Machzakinan Issura for a mere Chashash. [See Aruch Hashulchan 122/20]
Is there a difference between if one left the vessel by the gentile’s home or left the gentile in one’s home alone regarding Bedieved? The Michaber and Rama ibid entirely deal with a case that one brought his vessel to the hosue of a gentile, and only in the end does the Rama conclude that one is to be stringent Lechatchila even when leaving a maid in one’s home. This seems to imply that they have different laws Bedieved. If correct, this would explain why in 118/12 no mention is made in Poskim regarding Bedieved, as is done here. See also Taz ibid and Mordechai ibid who seem to differentiate and say that in the Jews home we do allow the Sfeik Sfeika to permit using the vessel after 24 hours. However, see Mordechai ibid who concludes even by knives in Jews home “Venachon Lehachmir.” See also Igros Moshe ibid who makes no differentiation between the cases and applies the Bedieved ruling of here to a case where a gentile was left in one’s home for some time. Vetzaruch Iyun!
 As it takes time for the gentile to cook his food and hence enough time must pass for one to be able to question whether 24 hours have passed since his first use. [See Rama ibid who directly implies this] However see Shach ibid whose wording is “If it stayed by the gentile for 24 hours..”; See Mahariy Bruno 27, brought in Darkei Teshuvah 122/40 “Stayed by gentile for two days”
 Rama ibid; Shach 122/8; Taz 122/8; Mordechai ibid
The reason: So long as 24 hours have not passed since the gentile could have possibly used the vessel, then there is only one doubt, which is perhaps he used it and perhaps he did not. [Rama ibid] Alternatively, we assume the gentile used it, and it is not considered a doubt at all. Nevertheless, what is a doubt is whether he used it for a food that is Pogem or not. [Taz 122/8 in negation of Ram’s doubt; Mordechai ibid]
 Rama ibid; Taz ibid
The reason: As there is only one Safek, perhaps he cooked food in t or perhaps he didn’t, and by a Biblical doubt one must be stringent. [Rama ibid] Alternatively, we assume for certain that he cooked in it, and the doubt is whether he cooked a Davar Pogeim or not. [Taz ibid; Mordechai ibid]
 Rama ibid based on Svaras Atzmo; Poskim brought in Darkei Teshuvah 122/40; Aruch Hashulchan 122/20 and that so is implied from Shach ibid
The reason: As one can argue that even here there is a Sfek Sfeika: a) Perhaps he did not cook in it at all, and b) Even if he did, perhaps he cooked a Davar Pogeim. [Poskim brought in Darkei Teshuvah 122/40; See Taz ibid] Alternatively, as the entire matter is a mere Chashash, and thus Bedieved Lo Machzikinan Issura. [Aruch Hashulchan 122/20]
 Taz ibid; Mordechai ibid; Aruch; Beis Lechem Yehuda 122/9, brought in Darkei Teshuvah 122/40
 Chamudei Daniel Taaruvos 7, brought in Darkei Teshuvah 122/42, that so is implied from Setimas Haposkim
The reason: As perhaps the non-Kosher food that was cooked is Pegam in the new food. [ibid]
 Rama 122/9 as explained in Shach 122/8 and so is final ruling of Shach ibid; Reah; Toras Chatas 59/4; Taz 122/8 regarding if left by gentile Beshogeg
The reason: As within the 24 hours there is only a single Safek; whether he used the vessel for non-Kosher or not. [Rama ibid] This doubt is a Biblical doubt. However, after 24 hours from the time it began staying with the gentile it is a Sfek Sfeika, as a) Perhaps he did not use it at all and b) Even if he did perhaps he used it 24 hours ago and it is no longer Ben Yomo. Now, throughout the entire Torah we permit Sfek Sfeika even by a Biblical prohibition. [Implication of Rama ibid; See Taz ibid] Alternatively, we definitely assume that he used the vessels for non-Kosher food and the Sfeik Sfeika is as follows: a) Perhaps 24 hours have passed since he used it and b) Even if used within 24 hours, perhaps it was used with a Davar Pogeim. [Taz ibid based on Mordechai ibid]
Other opinions: Some Poskim rule one may not use the vessel even after 24 hours, and hence if made of metal it must be Kashered, while if made of earthenware it must be destroyed. [Implication of Mordechai, brought in Taz ibid; Implication of Issur Viheter, brought in Shach ibid; Bach 122 and 137] Some Poskim rule it is never permitted until 24 hours pass from the time it was retrieved from the gentile. [Chesed Leavaraham Kama Y.D. 40, brought in Darkei Teshuvah 122/40]
 See Chesed Leavaraham Kama Y.D. 40, brought in Darkei Teshuvah 122/40, who establishes the case of allowance to be only when 24 hours pass since retrieving from the gentile, as perhaps he used it towards the end of the day. See also Igros Moshe ibid
The reason: As now we know for certain that 24 hours have passed since a last use and the entire doubt is only Rabbinical, as after 24 hours the taste is Pagum and is only Rabbinically forbidden. Now, by a Rabbinical doubt we rule leniently. [See Shach 122/8 in name of Maharash Mebonburg]
Other opinions: The above stringent Poskim are stringent even in this case, as no differentiation is made. Seemingly the reason is as suggests the Taz ibid as we never allow one to initially rely on a Safeik.
 Taz 122/8; Other Poskim who are stringent after 24 hours [but make no distinction of Shogeg/Meizid]: Implication of Mordechai, brought in Taz ibid; Implication of Issur Viheter, brought in Shach ibid; Bach 122 and 137
Is there a difference between if one left the vessel by the gentile’s home or left the gentile in one’s home alone? See Taz ibid and Mordechai ibid who seem to differentiate and say that in the Jews home we do allow the Sfeik Sfeika to permit using the vessel after 24 hours. However, see Mordechai ibid who concludes even by knives in Jews home “Venachon Lehachmir”
 The reason: As we never allow one to initially rely on a Sfek Sfeika [or Safeik Derabanan]. [Taz ibid]
 Igros Moshe Y.D. 3/61
 Shach 122/8 [towards end]
 Aruch Hashulchan 122/20
 See Michaber 136/1; Shach 122/8; Taz 122/8
 Aruch Hashulchan 122/20
 Shach 122/8 and 136/3
Other opinions: Some Poskim rule one may use the cup after 24 hours. [Bach 122 and 136, brought in Shach ibid]
 Rama ibid; Mordechai in name of Rabbeinu Tam; See Shach 122/8; Taz 122/7
 See Michaber 119/7 that such a Jew is like a gentile for all matters and is hence Chashud for everything; See also Michaber Y.D. 2/5 and Admur ibid; Regarding a Jew is keeps Shabbos but eats non-Kosher: See Michaber 119/3 that one who is Chashud to eat Treif is not Chashud to steal Treif; See Rama 1181 and Shach 118/16
 The reason: As many Poskim hold a Michalel Shabbos of today sdoes not make wine Yayin Nesech.