I've come close to killing my PC's a few times, and while I'm willing to hand wave a lot of rules I don't want to accidentally kill my PC's due to a rules fail so I decided to nail the rules of death and dying as much as I could.
Being a programmer I struggle with the prose style of some rules so I decided to translate the "Injury and Death" section of the CRB into something more algorithmic and ended up with the following flow chart to consult whenever a player hits zero HP.
It has a number of entry conditions across the top and you follow it from there answering each section or taking the the action.
Green lines mean yes/action taken and red lines mean no/action not taken.
A lot of the healing options are optional, as even if you have resolve points or a medic nearby you/they can chose to let you die.
You might not understand it all if haven't read the CRB section in detail yourself at least once as the items in each box are shorthand.
I'm sure it has some mistakes so if you spot anything let me know, but double check the rules first because in some case while not explicitly stated in a section, its the logical conclusion of items written in separate sections (which is why prose for rules always irks my programmer brain ;-) )