Qitzur Shulchan Arukh – 182:14
But in any case, it is permitted for a member of someone’s household to give a slice [of food] to a poor person, or to the son of one of the homeowner’s beloved [friends or relation] without his knowledge because that is the custom of homeowners. It is not called “without the owners’ knowledge” since that is the custom and the owners know of this custom. For this reason, it is permissible to receive charity from women, a small thing, without knowledge of the owners [ie their husbands, assuming they didn’t agree to communal property], since this is their usual way, and the owner knows that this is their way. Similarly in an orchard, if it is usual for him to eat from its fruits on the general knowledge of the owners [without this specific incidence discussed] it is permitted. Similarly anything like this.
Related to this halakhah of being able to assume the owner agrees to customary practice, R’ Daniel Eidensohn pointed me to an answer to a question I asked about 182:12:
This situation comes up in shul pretty often. There aren’t that many different styles of men coat, and it sometimes happens that someone looks through the coat room and realizes that the only remaining coat was one similar to theirs. Someone who left already took with the wrong coat.
I hadn’t heard, though, of a rabbi telling the person stuck in this situation that he is not permitted to wear the accidentally exchanged coat home.
Rav Moshe Feinstein (Igeros Moshe vol VII, Orach Chaim vol V, #9, sec 7, pg 15) opens by saying that use of the other person’s coas is prohibited. He cites Bava Metzi’ah 46a and Shulchan Arukh, Ch”M 136:3.
Then the Igeros Moshe cites the Arukh haShulchan (end of 136; hereafter AhS). The AhS rules that since wearing
the other person’s galoshes or coat is the customary response, one can assume that the owner implicitly gave permission.
Rav Moshe then sets limits. Like the fact that if the baal were to demand repayment for the value of coat rental, you would be obligated to pay it. (I wonder if that’s on Shabbos too, since that would imply a he leased you his coat on Shabbos.)
And Rav Moshe notes that since we only see this in the AhS means there must be communities where this is not the minhag. And therefore shuls that have this practice should announce it (and put up a sign, say so in the stickers in the front of shul siddurim, and things of that sort…)