Unless made to stand in water, cacti are just about impossible to kill.
One of my professors who did research on cacti had a greenhouse filled with unique and rare succulents from all of the world (more a personal specimen collection than research subjects). His philosophy was, "Other than water, light, and temperature, no interference!" If a plant fell over, he let it stay fallen over. He didn't prune them or rearrange them.
There were several that had fallen over probably 10 years ago and had recorrected themselves, growing straight up once again. You'd be surprised what natural things can live through. We're so careful to "take care" of our plants, but if they fall over or get soaked in water, they'll probably be okay.