I think its because your question is all over the place and bc it's scenario driven.

If there is a lease for a tenant and the property is sold.... The new owner must honor the lease unless a) the new owner plans to move in or b) the lease has a clause saying it wouldn't be transferred. (This is general there are always specific scenarios. I haven't read laws in CT revently tho to see if B is still an option).

In this case there is no lease. The current owner would honestly be stupid to offer a lease is they want to sell.

Your girlfriend should look for a new place to live.