What can happen if a bird strikes the engine during landing?
A range of things can happen.
For an airliner with a modern turbofan engine, the mostly common outcome is, absolutely nothing happens to the aircraft (although the bird's day is pretty thoroughly ruined). A sparrow can be chopped up by the fan blades &amp; blown out the back, and the crew will never notice it.  The engine won't hiccup, and until somebody sees a trace of blood and feathers on the fan blade during a walk-around, nobody will have any idea it happened.
Next case is a small bird gets ingested into the core. Chances are good the engine will keep running (remember, small bird we're talking about here), although the crew may notice a fluctuation in the engine instruments and there may be the smell of cooked (charred) bird in the air conditioning system.
In both of these cases, the engine will be inspected; the case where the bird went into the core takes longer, because maintenance will have to use a bore scope to look inside the core to inspect for damage.
The worse case than either of these is a big bird (or several) going into the engine.  Depending on the specifics, the engine may chop them up &amp; spit them out without damage, or the fan blades may be damaged, and/or the core may be damaged, and in the bad case the engine loses power, and in the worst case, it quits.
Losing one engine to a birdstrike is quite rare and is a pretty big deal, but most certainly not unrecoverable. An airliner can fly fine with one engine shut down.
If the birdstrike happens on short final, the crew might simply use more power on the operating engine and continue on to land. If it happens farther out, they might continue or they might discontinue the approach, go around, shut down the damaged engine, and then come back and land.
The really, really bad case is where you get enough bird strikes that they shut down all engines, and at that point you're a glider.  If that happens at 50' over the runway, your only choice (land straight ahead) still gets you where you wanted to be anyway. If it happens farther out, well, that's where somebody gets to try to be Sully 2.0.  That sort of a scenario is extremely rare – like one in tens (if not hundreds) of millions of cases rare.
You're far more likely to get hit by a semi truck driving home from the airport than having your day ruined by a bird going through an engine.