It is unlikely to just stop. There would be a gradual wind down with the contrail most likely diminishing to nothing. This is due to the residual heat in the combustion chamber generating the trail but reducing in intensity as the temperature reduces to ambient.

The flame out is not visible. If you see something, it is something else. The normal ones are surge and stall which have similar characteristics to the MD-11 shown.

I meant it would just stop as in not sputter.
Jet engines do not sputter when out of fuel, the combustion simply stops.