My tenant behind in rent is moving out before contract expiration

[Abad Marroquin]

This tenant called me today Monday and said they are moving out on Wednesday because they don't want to be evicted. The husband had an accident and and did not work for a month and they said they would catch up once he would be back to work. They begged me to work with them by giving them  a payment plan. He is back to work now and now and his wife called me and told me about their intention to leave. They are late one month and a half ($1300). The contract is due on January 18th. I have a deposit of $400. Should I evict them anyways since they have not left the property or I just let them leave peacefully?

What abou the rent they are behind? Can I sue them for that? 

It's obviously I need to learn how to become a more effective landlord. Thanks for your input!