Something similar did happen in real life many years ago. Can't recall the full details but it was in an AAIB Bulletin.
It was a light aircraft inbound to the Channel Islands from the UK. Somewhere north of the Jersey Zone the pilot says he has a problem and is going down.
Jersey's radar is a lot better than realised though and it tracked the aircraft as it turned north and headed back to the UK. The target was very intermittent and this suggested the aircraft was at extremely low level.
Parts of the aircraft were eventaully found just offshore from the south coast.
Apologies for the vague details but it was a long time ago - possibly early 1980's.
jb