Tenant Early Termination

[Robin Bordon]

Hi, 

I am subletting my apartment in California to a tenant until the end of December but now wants to leave ASAP, within the first week of December. 

Their reason for leaving is health reasons which was made very transparent from the beginning. I collected a security deposit and said I would not penalize him for breaking the lease if it is due to a health related issue.

My question is: Is collecting the last months rent considered a "penalty"? Am I still entitled to the last months rent while I do my due diligence to actively find a replacement? 

I look to work with him and keep everything easy going but want to fully know my rights.

Thank you