The ‘stupid’ part was the fact that the F-117’s flying in from Aviano (Italy) flew the same track mission after mission. Allegedly they were tipped off as to the takeoff time by spies sitting near the base. Once your enemy figures this out they can trick-up a missile radar to ‘look for’ the stealth aircraft’s signature. These things aren’t totally invisible to radar, only difficult to ‘see.’ Bammo! 1 dead stealth fighter.
OTOH, the News footage of the cash site showed a lot of scattered burning wreckage. How much of the wreck was useful is open to question.
Large portions of the craft were recovered, from the engine intakes to the exhaust to critical joints and things like the canopy.
IIRC, cell towers were used to look for the moving radio “void” in a computerized and decentralized method.