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It is forbidden for a Jew to have any form of liability [even due to negligence] over Chametz during Pesach, if the Chametz is being kept in property that is owned, rented, or borrowed, by the Jew. It is permitted for the Chametz to be stored in the property of the gentile owner, or another property that the gentile owner arranged for it to be stored in.
A gentile acquaintance asked me to hold his Chametz for him in my home over Pesach until he returns from a trip, may I do so?
No, unless one explicitly arranges with him that he is not to be held liable for loss and damages even if he is negligent in guarding the Chametz.
If one is storing the Chametz of a gentile in his home, and he did not relinquish liability, does it help for him to perform Mechiras Chametz through a Rav to avoid the prohibition?
No. The Mechira only helps to remove one’s personal ownership over Chametz, and does not remove any liability that one may have on the Chametz of someone else. Thus, one must relinquish any liability from the Chametz in order to be allowed to store it in his home, even if he performs Mechiras Chametz. However, if one explicitly includes in the Mechira that he is also selling the gentile’s Chametz that he has liability over, then seemingly the sale is valid, and his liability ceases to exist. However, in such a case, he must pay the gentile back for the Chametz sold.
Do we retain liability over Chametz that remains in our home and was sold to the gentile through Mechiras Chametz?
Allowing the Chametz to remain in one’s home after the sale does not make it into a Pikadon, and does not make one liable for damages, even due to negligence, unless the gentile stipulated otherwise. [Thus, by a normal Mechiras Chametz sale in which the sold Chametz remains in one’s home, the Jewish homeowner does not carry liability.] Nonetheless, since it appears as if the Jew has accepted to store the gentiles Chametz in his home and has thus accepted liability, therefore, the custom is to include as part of the sale transaction, the renting of the rooms in which the sold Chametz is found, as now the Chametz is no longer in our property. [Some Poskim, however, rule that in today’s form of Mechiras Chametz, there is some form of liability that the Jew has for the Chametz that was sold to the gentile and to counteract this issue, part of the sale transaction must include renting the rooms in which the Chametz is found in the gentile, as although we remain liable, the Chametz is not in our property. However, according to the stringent opinion above who forbids to leave the insured Chametz even in a room rented to the gentile, this does not help.]
 See Admur 440:16 who permits selling the Chametz to another gentile in order to escape ownership due to liability, perhaps here too, if one includes in the Mechira any Chametz that he has liability over, then he no longer transgresses. To note that some Batei Dinim include in their Shtar Mechira that it includes also any Chametz that they have liability over. [See Piskeiy Teshuvos 440 footnote 13]
 See Seder Mechiras Chametz Levin p. 162
 Admur 448:7; M”A 448:4; Taz 448:4; Bach 448
 See Admur 448:7 “Nevertheless, if possible it is proper for the gentile to remove the Chametz from the property of the Jew before Pesach as otherwise it appears as if the Jew has accepted to store the gentiles Chametz in his home and has thus accepted liability of damage over it.”
 Makor Chaim 448:9; See however Sheiris Yehuda 8, brought in Shaar Hakolel 18 who counters this claim; Seder Mechiras Chametz Levin p. 162
 Makor Chaim 448:9