Engine failure on final

The discussion about cutting power on final reminded me of something
I've been puzzled about for some time now.

If you fly final with some amount of power (which I gather most people
do -- I always have) that seems to guarantee that if you lose your
engine on final you will land short, and there's pretty much nothing you
can do about it. Is that true? Or have I missed something? What
should you do if you lose your engine just after turning base to final?

rg