Ice?
Certain types of engine icing might lead to an unresponsive engine, and this could affect both simultaneously; or with decreased efficiency on one, the other engine struggles which might make it more susceptible to the effects of ice, so shortly after both are affected.
Although most engines are anti-iced, some of the big fans rely on fan-ice shedding (centrifugal action) at higher rpm. Thus during an approach with relatively lower rpm and in unusual conditions of a lengthy exposure to the ‘exact’ icing conditions (and possibly without engine anti icing) problems might be encountered.
IIRC the smaller fan F100 and 146 engines suffered fan icing in freezing conditions when taxiing – low engine speed. Some aircraft types also suffered from this in-flight (exceptional atmospheric conditions) where the situation was usually indicated with a Vib warning and cleared with an increase of thrust (within the temp limits).
Ice can affect the efficiency of the engine (mainly fan thrust); autothrust seeks to adjust thrust to maintain desired airspeed, the engine is reluctant to respond / insufficient thrust (due to the effect of ice), more thrust lever input, mismatch in fuel/air/engine speed ratios; - bad situation turning worse.
At what engine speed does a Gen come off line during an in-flight shutdown (normal shutdown – ice free windmill characteristics) or in a sub idle condition?