Can I collect past due rent after Cash for a keys agreement

[Josh Carson]

I am new to real-estate investing.  I have a tenant who immediately upon moving in told me she did not have money to pay the rent and applied for ERAP. She was approved and I have been paid but payment is consistently 20 days late and does not include the late payment fee. I issued a notice to quit and did not receive payment during that time. I offered her her security deposit in full to move in 30 days to avoid going to court. ERAP has since mailed a check for February rent. Can I still cash this next month if she vacates in 30 days? I know that in the future I need better screening methods, however am just trying to figure out the proper solution out of this lease for now.