Death note : What if L didn't die but light held him captive?

What if light did't exactly kill L? What if he had something to erase his name and bring him back? What if light kept L captive in a house and visited every day to talk and all that stuff? What if on the day that light was supposed to die...he told near that L was alive?

This story starts on the day light was to die. (possible different personality and different outcome or beginning to something)