I live in a molbilhome that's in my parents name and they nolonger reside here.is it leagal for them to rent it to me and keep it in thair name? Or is that subletting?

Is there a contract (lease or mortgage) which prohibits subletting? Otherwise, where are you getting the idea that subletting is somehow illegal?

If parents own the premises, and they rent it to child, no that's not sub-letting; it's letting (or renting to someone).

If parents are renting or leasing (from a landlord) and they turn around and let child live in the premises for rent, that's subletting.