Re: Former tenant liability when not dropped from lease
On the facts as given it looks to me as though you can defend against the claims and avoid liability. However, small-claims outcomes are unpredictible and don't necessarily always follow the strict letter of the law but rather the judge's personal view of who's right and who's to blame.
Further, there are facts missing. It is possibly important to know when the landlord became aware that your sister had replaced you as the co-occupant with your mother. If the landlord was clearly aware you weren't there, due to the names on the rent checks, or whatever other reason, you have a better case.
The analysis goes something like this. When the original lease expired, the tenancy became you and your mother, month-to-month. When you moved out, nothing changed, but presumably somewhere along the way, perhaps when the new lease was presented for signature, the landlord became aware that your sister had replaced you as the occupant. From that point onward, responsibility for the rent rested with your mother and your sister.
The question of who, if anyone, put up a security deposit is a complicating factor. If you made a deposit but never asked for it back, that could muddy the issue of whether you ever LEGALLY moved out and your sister moved in. It also gives the landlord a financial lever.
The real issue here, in my opinion, is whether there is unpaid rent and damage to the apartment. If so, then who is really to blame? If the judge can figure that out from the evidence given, the result will be proper, except that it sounds as though your sister wasn't named as a defendant.
Maybe your family should get together and work out the problem between yourselves, then present the landlord with a settlement proposal.