Pinworms certainly can be eliminated and gone. The body has an immune system after all, and pinworms are just acquired threadworms, and they can be expelled as larvae and mature worms. If a person maintains a suitable terrain, then eggs can be dormant and hatch later. It's all about susceptibility and health.
When healthy people (children especially) it's a test of their immune systems, but remedial efforts can eliminate them and their body's have resistance thereafter. If the terrain is unsuitable (e.g. a strong immune system) they will pass out of the body to hatch in more suitable environs. Plenty of cases of getting rid of them forever.
Note that the typical drug treatments don't impact the eggs, and then they come back when they're ready to hatch.