Depending on where you are, your lease might automatically convert to month to month. This exact situation happened to a friend of mine in NYC, they didn't sign the lease and didn't move out, and are just paying the old rent. They are legally month to month and are entitled to 60 days notice if the landlord wants them out or raise the rent (landlord hasn't said anything yet). A lease renewal != notice of a rent increase on a month to month tenant.