Bill Laskey did not go gently into that good night. After the Giants cut ties to him after his second stint by the Bay (after the 1986 season), he signed with the Tigers, but spent the 1987 season in the minors. Then he signed with Cleveland for 1988, made 17 relief appearances, and was released, again.
For 1989, Laskey and his mustache turned up in BoSox camp, as seen in this image from Larry Fritsch Cards. I guess he was an NRI, as there's no indication he signed a contract.
He didn't make the team, but did enough that the Royals signed him for Omaha. And in 1990, he ended up at Richmond (Braves) and in 1991 at Oklahoma City (Rangers). That's six different franchises in six consecutive seasons, not including this Spring in Winter Haven with the Sawx. Points for determination, at least.
(Bill's still connected to the game; he's a long-time radio host for KNBR in San Francisco and had been a post-game host for Giants games on NBCSN-Bay Area.)