Sounds just like the Soviet Flogger whose pilot banged out after a flame out in 1989. The engine relit, and it trimmed itself out and decided to auto defect.
The Flogger was intercepted by 2 x F-15Cs from Bitburg as it entered West German airspace, and the UK had a pair of Wattisham F-4s CAPing in the old Amber 37 airway (god did ATC whinge about that!!!) in case it went feet wet. Even the good old Bloodhounds got told to turn the keys in case the fighters lost it!!!
The plan was to shoot it down once it was over the North Sea and away from towns etc. Eventually, the aircraft continued all the way to Belgium where it crashed (tragically killing a Belgian youth) due to fuel starvation.
Regards,
M2