When there is no written lease, tenancy is month to month tenancy per an oral (sometimes called verbal) lease. When that's the case, as the term "month to month" is implied, either party can terminate the tenancy with one month's notice. That in turn means that the most a tenant could be responsible for is one month, if she gave inadequate notice...i.e. if someone said, "I'm moving out right now," they'd still be liable for the next month, but no longer than that. The important thing is, there must actually be notice--if your sister moves out without providing notice (preferably in writing, in some fashion she can prove delivery) that she's ending her tenancy, the landlord might be able to claim that she never actually ended her tenancy and therefore has a continuing liability until she does so.