Jet wash is exhaust gas and contains little oxygen. If the exhaust is “inhaled” by another engine, it may starve that engine of oxygen and cause it to flame out (like how the engine in your car would shut down if it couldn’t get oxygen). If one engine on an F-14 shuts down without the pilot preparing, and the other engine is running at a high power level, you get what’s called a thrust differential – one side of the aircraft is being pushed forward and the other side is not. That can put the plane into a flat spin. Imagine trying to control a canoe when everyone is rowing on the same side.
The recovery procedure would involve shutting off the working engine to remove the thrust differential, trying to get out of the spin, and then trying to re-light both engines before losing too much altitude.
Sorry I know this stuff – my dad flew F-14s and actually flew in a few scenes that made it into Top Gun. We had this discussion a few times.