Is it possible to not wake up from getting put under by anesthesia?

Possible? Rare: By not wake up, do you mean die? It is extremely unlikely that a generally healthy patient having minor surgery (e.g. Middle-aged person with high blood pressure having hernia repair) would die from general anesthesia performed by trained clinicians in a modern facility. It is so unlikely that we are not sure of the exact risk, but we think it is 1 in 250000 anesthetics.

Rarest complication.: Such a disastrous complication is very rare. Estimates are around one in several hundred thousand. You are much more likely to get struck by lightning. The sicker you are to start with, the higher the risk.

Very Unlikely: Despite sensational movies or book, anesthesia is incredibly safe today. The risk is thought to be about one in 350, 000. I tell patients that it is more dangerous to drive to the hospital for the surgery than to have the anesthesia.