Yes, we can accept a retired guarantor as long as they're aged 19-75 and haven't had trouble paying bills in the past. Although they do not have to be a homeowner, it may increase the possibility of us accepting them as a guarantor if they do own their own home.
The guarantor will have to pay the loan back if the borrower doesn't, so they must be able to afford the monthly payments and still have enough money to live their normal life.