possessive pronouns

I think it's worth echoing the wisdom of @EducationAisle's response. It is not technically a grammatical error for a non-possessive pronoun to refer back to a possessive noun. We've seen an OA or two where this has happened, so you wouldn't want to blindly eliminate an answer choice on this basis.

The potential problem is if the construction creates an unclear meaning. For example:

"When Tim's cat peed all over the living room carpet, he began to contemplate what life might be like alone."

Is "he" referring to a "cat" that's had enough of its tyrannical owner? Or to "Tim", who is tired of having pets that make a mess? You wouldn't necessarily eliminate an answer choice right away on the basis of an ambiguous pronoun, but if you had another option that was clearer - for example, "When Tim's cat peed all over the living room carpet, Tim began to contemplate what life might be like alone" - you'd prefer the clearer alternative.

I hope that helps!