Many military jets (and even many commercial) can fly on only one of their engines, why the Navy has insisted for so long on having two in its jets for decades encase one goes out the aircraft can still land back on the carrier instead of being forced to ditch in the sea and they where rather reluctant on having to only go with one engine for the F-35C (which they had to, to have a common design for all versions, but accepted it due to increased engine reliability and cost).
But if an AA missile hits a jet, it is pretty unlikely all that missile is going to do is just knock out one of the engines, as the shrapnel is designed to do internal damage all over the aircraft to the hydraulics, fuel lines and so on leaving the entire aircraft crippled, not just one system, and also the aircraft is likely to be structurally compromised as well.
Although yes it depends on what type of missile we are talking about as some don't even have a proximity fuse with shrapnel warhead on them and rely largely on the kinetic energy they inflict on the target (like the Rapier missile).
But going back to your main point about jets being able to fly on just one engine, it should be noted that once they are down to one engine they become combat ineffective, with most likely having to dump all their ordinance they are carrying just to keep airborne and would be flying at a significantly reduced speed from having 1/2 their power gone and having to lug around a dead engine, so they wouldn't be able to strike targets and all they could hope for is to get back to a freindly airbase if they are lucky.
As terms of what we could do ingame with the BF2 engine, using python we may be able to give a % chance of an engine failure after taking xxx amount of damage, similar to how we track vehicles, but dunno if we could make it so that aircraft with two engines could stay airborne at reduced speed on just one (with still a % chance of both engines failing), but you would have to talk to our python coders about that and may require the jet to be coded with two engines which may require a second networkable and many of our jets don't have any free networkables to spare. I also seem to recall that the python disabling code doesn't work on engines in MP (does in SP) but ye, you would have to talk to a python coder about that for more details but I remember dbzao doing similar code for choppers where tail rotors could fail and the chopper would spin out of control if they did, but it only worked in SP and not MP so was abandoned.