It continues to heal them unless they die in which case the fast healing stops.
I believe that it shoud stabilizes the pc as a cure minor wound does the same, but I don't have my books with me. The one thing I'm not sure of is on the pc's first turn unconsicus does the bleeding or the fast healing take effect first. If the former takes place first the pc may die if at -9 when he had an ability that could save him. If the latter takes place first the bleeding never happens as the pc is stablilized.