As an alternative to the nonpayment of rent eviction process, you may be able to recover possession of the rental unit by delivering a belief of abandonment notice. When rent is due and unpaid for at least 14 days and you believe that the tenant has abandoned the property, then you may serve the tenant with a Notice of Belief of Abandonment. (CA Civil Code Section 1951.3).
If the tenant does not respond within about 18 days after the abandonment notice is served, then the rental unit is deemed abandoned and you can recover possession of the rental unit.
With regard to abandoned personal property, that requires a separate and additional notice after you get possession of the rental unit. (CA Civil Code Sections 1980 - 1991)
Yes, you can evict them for failure to pay rent. It is unfortunate that they are in the hospital, but that does not excuse them from paying their rent.
As for what to do with abandoned property, there is a process that you need to follow. I suggest you go to the Department of Consumer Affairs website and look at the tenant rights booklet. It explains what you as a landlord can and can't do and how to do things properly. As a landlord, you should probably keep a copy handy.
You might also want to contact a local attorney regarding the hospitalized tenant. There may be local rent control requirements that limit what you can do.