Termination is the most commonly used technique; in this case the orphan is killed.
Reincarnation is a technique in which machines periodically try to locate the parents of any remote computations; at which point orphaned processes are killed.
Expiration is a technique where each process is allotted a certain amount of time to finish before being killed. If need be a process may "ask" for more time to finish before the allotted time expires.