As said earlier, one of his henchmen takes over.
I don't think that his family had a candidate that could take over the country in 1986, it's clear now that Gaddafi is/was looking to put one of his children in power as his successor. Libya more or less continues the historical path it did to the modern day.
Question I would wonder about, what effect would this have on state-sponspored terrorism. Would the leaders of the other countries come to the conclusion that an air strike by the United States could "accidentally" kill them if they acted up too much and act accodingly?