Cases that a Peruzbal is not required:
If one lent money in exchange for an object from the borrower to serve as collateral for the loan then the Shemitah year does not abolish this loan [and a Peruzbal is not required].
If the collateral is worth less than the amount of the loan may the lender still demand the entire loan? Some Poskim rule that one may only demand payment for the amount of worth of the collateral and not any more. Others however rule that the entire loan is collectable.
B. Due date of the loan is after Shemitah:
If one loans money to his friend and sets the due date for after Shemitah, then the Shemitah year does not abolish the loan [and a Peruzbal is hence not required]. Thus a Peruzbal is only required for a loan that is due to be repaid before the end of the Shemitah year and the borrower has not yet done so.
C. Charity organizations:
Charity organizations that are owed money are not required to perform a Peruzbal in order to collect the money after Shemitah. [This however only applies to charity organizations that cater only to paupers, such as the local charity fund for poor families. However those institutions of Chesed [Gemach] that cater to all people, whether rich or poor, have to perform a Peruzbal.]
Does a loan that was given in the Elul before Shemitah with an unspecified due date require a Peruzbal before Rosh Hashanah of that year?
Does a Shul have to perform a Peruzbal in order to collect pledges that they are owed?
Does a Yeshiva have to perform a Peruzbal for tuition payments that are owed to them?
Those tuition payments that are on credit do not require a Peruzbal. However those tuition payments that are due before Rosh Hashanah of Shemitah and have been sent to the parents seemingly require a Peruzbal to be performed.
 Admur 38; Michaber 67/12
 The reason: As the verse which states that one is not to demand the loan is inapplicable in this case as he does not need to demand the payment and can simply take the collateral. [Admur ibid]
 Michaber 67/12
 Rambam 9/14; First opinion in Michaber ibid
 Tur in name of Rosh; Second opinion in Michaber ibid
 The reason: As since the collateral was taken in exchange for the entire loan it is therefore considered as if he has the entire loan in his hands. [Smeh 67/24]
 Admur 39; Michaber 67/10
 The reason: As the verse which states that one is not to demand the loan is inapplicable in this case as he cannot demand the loan yet in any event due to that the due date has not arrived. [Admur ibid]
 Michaber 67/28 “One who owes money to a charity fund, Shemitah does not annul the loan”
 The reason: As the Beis Din is considered the collecting agency of all charity organizations and hence the loan is considered to have been automatically handed to the Beis Din as soon as it was issued. [Smeh 67/50]
 Grach Naah in Yagdil Torah 25 p. 81; See Nitei Gavriel 11/3
The reason: As one cannot say that the Beis Din is the collecting agency of the owed money in such a case as this only applies to the money owed to the poor. Now, although there is no specific person in the organization that is owed the money nevertheless this is not enough of a reason to exempt them from making a Peruzbal. [ibid]
 Minchas Chinuch 477; Rashash; Poskim brought in Nitei Gavriel 16/4
 Bach 67/13; and Poskim brought in Nitei Gavriel ibid; Grach Naah and Poskim brought there [see Yagdil Torah 25 p. 79]
 Rebbe in Likkutei Sichos 12/256
 Aruch Hashulchan 67/8
 The reason: As pledges are considered a vow and not a loan and hence play no relevance to Shemitas Kesafim. [ibid]
 As it is similar to the wages of a worker in which case if the worker gives credit to his employer a Peruzbal is not required.
 See Nitei Gavriel 13/5 who writes they never need a Peruzbal, Vetzaruch Iyun Gadol as if they already asked for the student to pay tuition and he has not done so, this should be considered like a debt. Now although a Mosad Chinuch is like a charity organization, nevertheless since it is not only for paupers a Peruzbal should be required, as explained above from the Grach Naah regarding a Gemach.