An answer to your questions requires a lot more info.

Mainly, what State you are in. To me, it sounds like you lucked out and should go away without making a hassle.

On the other hand, if there were no charges against you, and no official documentation from law enforcement of any wrongdoing, then you may be able to stay.

In my area of California, once you live in a rental for over 2 years, the landlord has to give you a reason to terminate your tenancy - even if it's month to month. In other words, they have to have "cause" to terminate your tenancy. That's not always easy to do. In California they have to go through a legal eviction (unlawful detainer) process through the court system, which can be a pain in the ass.

And yes, in California landlords have to document the damages being claimed.