If you are a landlord and need money to keep your home, you will have a hard time finding a tenant to prepay a lease for a full year. However, there are a lot of people with poor credit due to the current financial/housing market and some of them do have cash. So, you might find someone who really needs a rental, but has bad credit and would be willing to give you a large chunk of cash to put down towards rent.
Do you mean would a renter pay upfront for the full 12 months to rent your home? If so, not likely....That's a lot of money to lay out all at once. At $1200/month thats $14,400 to lay out. If I had that kind of money laying around I probably wouldn't be renting I would be buying.