Nurse here.
If you're having a general anaesthetic for a routine operation, and worried about dying while under, please be aware there are about 7 different "levels" of stuff we can do to bring you back.
So if the thing we normally do doesn't work, we've got plan B, then we've got plans C, D, E, F, G& H. ( and we rarely need to even go to Plan C, let alone the rest!)
It's ridiculously rare for you to never wake up from a routine op, of course it happens occasionally, but for every case you've heard about it happening, there's THOUSANDS of identical operations where it didn't. I've been qualified 15 years and it's literally never happened anywhere I've worked.