I have a story about that, from the movie producer Fred Zinneman.
He was working on a movie and cast some paraplegics. One when asked said it was an accident, but didn't want to talk. Fred eventually got the story out of him.
He had been a paratrooper in WW 2. His parachute didn't open. But he landed in a big tree. Shaken, bruised, scratched up, and so on, but basically fine.
Climbing out of the tree he fell, and broke his neck.
Nitpick: The parachute likely opened _partially_ (as is common for such malfunctions) so that impacting a tree wouldn't cause injury or death.
That said, falling out of the tree checks out because that _is_ dangerous. Modern US Airborne training teaches a whole lot of caution when doing so. Best case you wait for someone to extricate you, but worst case (or for a combat jump), you deploy the reserve chute and then slide down it like a rope.
I don't know if they were using reserves in WWII (might have depended), but combat jump altitude is typically too low to have time to deploy your reserve. Better to chance the landing, than a hail storm of lead from the ground.
In WW 2, only US paratroopers had reserve chutes. This was likely a British paratrooper. So no reserve chute.
And yes. Climbing out of a tree while shaking from adrenaline is scary dangerous. But it is the sort of risk that takes experience to appreciate. In WW 2, nobody had experience.
He was working on a movie and cast some paraplegics. One when asked said it was an accident, but didn't want to talk. Fred eventually got the story out of him.
He had been a paratrooper in WW 2. His parachute didn't open. But he landed in a big tree. Shaken, bruised, scratched up, and so on, but basically fine.
Climbing out of the tree he fell, and broke his neck.
It's the landing that does it, not the fall.