Tenant terminating lease early

[Nataliya Isupova]

My very good/responsive/responsible tenant decided to move to a bigger place. They found a new place, Moved after 2 weeks from the time they first told me about it.  They moved out 1.5  months earlier before the end of their lease with me. I said ok to moving earlier, as long as they’re responsible for their remainder of the rent to me until I find someone else. 
A month later, I’m still searching, having a lot of interest but no one willing to move in earlier than when my tenant’s lease ends.
My tenant just asked me if I can terminate their lease 15 days earlier - basically asking me to forgive a half month rent. Thoughts? Is it something common to do/ask? I personally have never had it happen before and curious to have some advice/feedback.