So as we know, Apex Legends is set in the Titanfall universe. In Titanfall, pilots which are too old or otherwise aren't as fast as they used to be could undergo a Regeneration.
Pilots that are killed can instead be turned into a Simulacrum. That's what happened to Revenant. They're programmed to believe they're still human. (Revenant's programming failed, he was turned into a Simulacrum against his will and he cannot die. So that's why he's mad. Anyways…)
Anyways… what method do you think they use in Apex Legends? It's set around 30 years in the future after Titanfall 2. And it seems in that time, they figured out how to make immortal Simulacrums such as Revenant. Not to mention in Titanfall 2 they had time travel devices.
Maybe it's a simulation? Maybe they're got a bunch of bodies ready which the legend's mind is transferred to when they die? Or perhaps they die for good? What do you think?