Looks like time has come and gone on your question, wish I was around when you posted this. Anyway, you are not in a good position, but, you are not in a bad one either. IF you are current on your rent, and you have not done anything terrible in past, I would wait till told otherwise.
It cost a lot of money for a landlord to rent out an empty unit. Most of us have to clean, fix, and advertise. It cost us a lot of money to evict someone too. What landlords want to see are stable families that are going to be there, always.
I miss my family that was with me for over 15 years! Good people! But, if the new landlord say sign a lease, do it. For in the lease there is usually a clause that states 'to airs and successors' meaning the transfer of property going from one landlord to another will not interrupt your enjoyment to that abode you live in.