Hiring a nurse or caretaker for the old or ill-Male versus Female:

Opposite gender-Male and female nurses:[1] It is permitted for a man who is sick to have a female caretaker. This applies even if the caretaker will need to perform intimate tasks, such as changing the person and helping him go to the bathroom.[2] However, a man may not be a caretaker for a woman who is sick if doing so involves dealing with the [intimate[3]] parts of her body, such as to clean her, and help her use the bathroom.[4] If however, it does not involve dealing with [the intimate parts[5] of] her body, there is no prohibition for a man to be a caregiver for a woman.[6] [He may even help her get up and lie down, and help her in non-intimate matters of the like.[7] All the above refers to a caretaker or nurse, however there is never a restriction against having a doctor of the opposite gender render even intimate medical treatment on behalf of the patient, and thus is permitted for a woman to have a male gynecologist.[8]]

Yichud:[9] When a patient has a caretaker of the opposite gender, care must be taken not to transgress the laws of Yichud during the visitations. Thus, one must provide either a Shomer [spouse/child] or Pesach Pasuach [open door or give keys to neighbors] to insure the laws of Yichud are not broken. If the male patient is in a coma or unconscious, there is no Yichud prohibition at all in any case. If a male patient is conscious but is impotent due to his illness/weakness, one may be lenient in Yichud in a time of need. This especially applies if there are no expectations of recovery.[10]  

Parent: If one’s parent needs a caretaker, the children are to try to take care of them. If they are unable, they are to hire a caretaker to deal with him/her.[11] Payment for the caretaker is the responsibility of the ill parent, although if they do not have money, the children are obligated to pay as a form of Tzedaka.[12]

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[1] Michaber Y.D. 335:10; Miseches Semachos 12

[2] Taz 335:5

The reason: As when the man is sick, he does not have any lust or ability to have an erection, while a woman does not have such a strong Yetzer Hara and hence won’t become aroused. [Taz ibid; Birkeiy Yosef 335; See Shach 335:9 in name of Derisha, Bach and Dakei Moshe] Alternatively, even though a woman may become aroused and have forbidden thoughts as a result of the tasks, there is no prohibition involved as women are not prohibited against masturbating and causing their own Zera Levatala. [Birkeiy Yosef ibid] Alternatively, when the woman is healthy, she can control the situation and prevent any wrongdoing from happening. [Beis Yosef and Levush, brought in Shach 335:9; Beir Hagoleh 335]

[3] Shach 335:9 in name of Derisha 335, Bach 335 and Dakei Moshe 335 that only by a stomach illness was this prohibition stated as “When she uses the bathroom, he sees her in both front and back” however by other illnesses it is permitted; Birkeiy Yosef 335 that so is implied from Michaber ibid

Other opinions: Some Poskim rule it is forbidden for a man to care for a female patient even if it does not involve dealing with the intimate parts of her body, but involves touching her body. [See Taz ibid who implies that even other bodily contacts which are done on a constant basis can lead to erection and is therefore forbidden. According to the Beis Yosef and Levush brought in next footnote, it is always forbidden whenever the female patient cannot prevent being taken advantage of.]

[4] Michaber ibid

The reason: As this may lead the man to get excited and have an erection, as a man has a stronger lust than a woman. [Taz ibid; Shach 335:9 in name of Derisha, Bach and Dakei Moshe] This can then lead to Zera Levatala. [Aruch Hashulchan Y.D. 335:1] Alternatively, when the woman is sick she cannot prevent him from taking advantage of her against her will. [Beis Yosef and Levush, brought in Shach 335:9; Beir Hagoleh 335]

[5] See Poskim in previous footnotes

[6] Taz ibid; Shach 335:9 in name of Derisha 335, Bach 335 and Dakei Moshe 335

[7] Birkeiy Yosef ibid; See previous footnotes

[8] See Michaber E.H. 23:3; Darkei Teshuvah 157:8; Apei Zutrei E.H. 23:8; Nishmas Avraham Y.D. 195:11; 23:5; Shevet Halevi 3:186; 4:167; Shiureiy Shevet Halevi 195:274; Minchas Yitzchak 7:73; Igros Moshe E.H. 2:14; Tzitz Eliezer 19:4; Taharah Kehalacha 7:1; Halichos Bas Yisrael 7:17; Ohel Yaakov p. 286; Encyclopedia Refuit Hichatit Erech Zera p. 388

[9] See Nitei Gavriel Yichud 5:3-5

[10] See Kiryas Melech Rav 2:22; Nechpa Bakesef 64; Tuv Taam Vadas Telisa 1:5; Igros Moshe E.H. 4:65-10; Otzer Haposkim 20:5; Nitei Gavriel ibid

[11] See Michaber 240:10 regarding a parent who lost their mind; Shemen Hamur Chelek Haderushim p. 111; Zera Emes 2:148; Kneses Yechezkal Mareches Chaf; Implication of Kiddushin 31b; See however Machaneh Chaim 2 C.M. 29 who implies that a son cannot delegate the mitzvah to another

[12] See Rama 240:12