An unlawful detainer suit is for possession of the premises. Please see the guide linked below for a "how to" book on evictions.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
You would file an unlawful detainer action to obtain possession of the property.
You could thereafter file an action for breach of lease to recover your damages.
I would strongly urge you to consult immediately with a litigator skilled in this area of the law.
PLEASE NOTE THAT THIS RESPONSE SHOULD NOT BE CONSTRUED AS A LEGAL OPINION OR ADVISE, AND DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP. IN ORDER TO RENDER A LEGAL OPINION OR ADVISE, THE RESPONDING ATTORNEY WOULD NEED FAR MORE INFORMATION THAN HAS BEEN PROVIDED, AND WOULD NEED TO BE RETAINED PURSUANT TO A WRITTEN FEE AGREEMENT.
If a landlord were strictly suing a tenant or former tenant to recover a judgment for damages to the leased premise, by definition it wouldn’t be in the nature of an unlawful detainer action.
But the landlord who brings an unlawful detainer lawsuit for ejectment of the tenant and to recover unpaid rent can certainly add a separate count to the pleading asking to be compensated for such damages.
