Won’t renewal the lease, what if tenant won’t move?

[Nina Zou]

Tenant always pay late, this month rent hasn’t been paid up to now. Just served eviction notice today. The Lease will be due by the end of March.

I know that I won’t  renewal them and I also know they don’t want to move, but they can’t afford the rent as far as I could see.

So my question is: what if they refuse to move after the 60 days notice that the lease won’t be renewed? 

Shall I stop accepting rent if they refuse to move but keep paying after mid month?