Should I evict in the last month of the lease?

[Dan Miles]

My tenant (inherited from last landlord) is late with rent for the second month except this month they are unresponsive to text and phone calls.  I went by one day and nobody came to the door.  They already told me they would not be staying due to the proposed rent increase.  Now, do I start proceedings to evict?  Do I need to worry about them trying to stay past the termination of the lease?  If they did stay over I would have to start eviction anyway right?  Any advice would be great!

Thanks!