When we were small and essentially self managing our own properties I used to do something different for each person depending on their attitude, the situation, etc.Since we have grown and have employees we had to make standard operating procedure and have to stick to it. 

County and law school libraries also have examples of forms and procedures.

As a proud Lexingtonian, I'm happy to offer insights into what I consider one of the finest cities in the country.

What is the correct procedure if the property is empty by March 1st but I never got the keys back?

Depending on the location in NY there will be a different tolerance "strictness" when it comes to following the eviction procedure.

Yes, one can, but the procedure is complicated.

I think in VA if it's in question, I have to post notice that tenant must notify me in writing within 7 days if they intend to stay and if no response, I can assume it's abandoned and follow next procedures for turnover and security deposit. 

So going over the lease and the duties and responsibilities while we sign it is part of our onboarding procedure and tenant training!

Assuming they're refusing to pay, pore over every detail of your lease and proceed with exactly the processes called out by it (and get advice from your lawyer concerning State laws/procedures to follow in case they may trump your lease terms). 

Specifically, ALWAYS work on providing safe conditions and law-abiding procedures.