Is my sister considered a tenant of my moms house in Pennsylvania?
It would depend on the exact agreement between the oarties but in the UK the answer is likely to be no. Your sister would have some type of protected tenancy for life and could not be evicted without a court order and a judge here will always support the tenant. No lease required if a tenancy can be assumed by the circumstances and in this case the written agreement and the payment of bills & taxes and simple uninterrupted occupation & control of the premises would suffice. Your mum could sell the house but with no income coming in its likely to be at a fraction of the vacant possession value - I normally work on 25% - 50% depending on the age of the occupier. In addition in the UK in such circumstances if the occupier had children, husband or close relatives living at the house looking after them they are entitled to protection as well! I have dealt with these in the past and the only solution is to pay the occupier to leave.