I always love to read this stuff as all the training is done on the basis that the engine will fail somewhere 'convenient'. It doesn't.
The two occasions the donkey has stopped on me have both been at less than 150 feet (one on finals and one on the go-around from a PFL) in an aircraft with the glide-ratio of a brick. I can assure you that your options are distinctly limited and your response has to be totally reflexive. Nose down to fly, nose up to flare, land (straight ahead). It all takes less than about 10 seconds. No time for any vital actions, checks etc. (though I did get a radio call in on the second one).
If you are already slow on final somewhere near the bottom of the drag curve, the nose has to go down very long way to keep flying which requires a fair bit of confidence at such a low altitude.
A good simple rule of thumb is "if you don't stall you won't die".
I was lucky enough on both occasions that there was clear ground under me and I was able to fly the plane away again later in the day.
Partial engine failures and rough running are another interesting situation seldom taught or thought about.
Teach your students to expect the unexpected.