Tenant breaks lease earlier, claiming to have sent me notice.

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Here is the story. My tenants were 2 days late on the rent, when I texted them with the unavoidable question I got a reply "Hi, I sent you a memo back in June that we were leaving mid. August "

What??? I never got any memos. And how can I prove that???

Turned out the tenant's husband got cancer for the second time, which was the reason for them to lose their house years ago. From her words she doesn't know how long he got to live.  They can no longer stay at my property. 

My husband promptly posted Notice to Quite on there door, to protect ourselves in case they would not move out like they say. I was instantly excused of being unprofessional and heartless. 

Now they have to pay $ 2000 in early termination fee according to the contract. I know I will never see that money. And I know they will probably ask for the deposit back.

I feel very bad. After all they were alright tenants.

What would you do  next?