Check and see what edition the player is playing or really likes. That'll tell you a good amount about what types of death they find acceptable.Allow me to go a step further, then.
What type of player death risk is tolerable?
Is it just the ones where no agency is had between how their character dies? If so, does that include the swing of dice?
What about deaths that occur because of a mechanic that players simply forgot?
What about deaths that were preventable but only through some obtuse method, like having counterspell to avoid the cleric getting PWK'd?