I mean, I don't think I've heard of a bird strike knocking the engine off a plane.

Oh, interesting. They even made a movie.

Once an engine breaks the question is whether or not it becomes unbalanced, that is one reason why they can become detached from the plane.

	▲	hshdhdhehd 2 hours ago \| parent \| next [-]
		Unexpected way to increase air safety: > In an effort to prevent similar accidents, officials captured and exterminated 1,235 Canada geese at 17 locations across New York City in mid-2009 and coated 1,739 goose eggs with oil to smother the developing goslings.[71] As of 2017, 70,000 birds had been intentionally killed in New York City through programs instituted after the ditching.[72]
	▲	kelnos 7 hours ago \| parent \| prev [-]
		The account on that page seems to indicate that the engines didn't detach as a result of the bird strike. One detached upon impact with the river, and the other was still attached.