Renter signed lease but now wants to change move in date

[Carolyn Walters]

I have a renter who signed a lease and turned in a security deposit to start renting at the beginning of July according to the lease. They signed it a few weeks ago. They called me today wanting to know if they could move in August 15th instead because one of them was diagnosed with cancer. So they want me to continue to hold it for them which would amount to half of June, all of July, and half of August without them paying. They signed a month to month lease.

What are my options at this point? 

Carolyn