Falling off a branch is, of course, a risk of living in the trees. It might seem an instant death sentence - and it can be - but one slip doesn't necessarily mean instant death, as there are a number of chances to... not die!
1) Clinging On
Slipping, or being shoved off a branch or similar treetop surface gives an initial chance to cling on and scramble back up.
"Clinging On" requires a DEX or STR save of DC typically 12, although this may be modified up or down at the DM's discretion depending on the exact situation - for example clinging on to a narrow smooth barked tree in the rain will be much harder than clinging on to rough bark on a wide branch overgrown with vines.
A failed roll implies that the creature actually does fall from the branch.
A successful roll means that the creature is Clinging On. While hanging on they may be treated as having the PRONE condition, except that it takes 3/4 of the creature's movement to get back to a standing position (unless they have a climb speed, in which case only the normal 1/2 movement is required), and the normally permitted crawling motion may be flavoured as swinging if appropriate. If caused to fall from "Clinging On" the following Clinging On save must be taken at disadvantage.
A natural 20 on the "Clinging On" save implies that the creature managed to grab something to save their balance at a critical moment and bring themselves back to standing in an appropriate space - they may continue to act as normal, and are not "Clinging On" or prone.
2) Grabbing Hold
While falling through the trees, there's a chance that a character might be able to grab a branch or vine to arrest their fall.
If a creature wants to try to Grab Hold as they descend they may use their action in their next turn after falling off to make an Athletics or Acrobatics check (they will only get one chance to do this due to how far you can fall in a 6 second round!) The DC for this is typically 14, but again may be made higher or lower at the DM's discretion depending on the exact circumstances.
A failure implies hitting the ground and taking falling damage (see below). Height from the lowest branches to the ground is typically 100', with the tops of the tallest trees being 400' or more from the ground.
A success implies being on a lower branch, "Clinging On" (as described above.) The creature will take half damage for the distance fallen - which can normally be considered to be 1d10 x 10 feet.
A natural 20 implies managing to land on a lower branch in a way that allows them to move as normal!
3) Falling Damage
Due to the thicker atmosphere and lower gravity of Eleath, falling damage on the planet is reduced to 1d4 per 10' fallen (as opposed to the RAW 1d6), capping out at 20d4.
Height from the lowest branches to the ground is typically 100', with the tops of the tallest trees being 400' or more from the ground.
This is delivered as bludgeoning damage on landing, with the falling character landing prone.
(Note that the high and long jump distances are not being increased for the low gravity, partly as the thicker atmosphere tends to offset that in these cases, and partly because they are already ridiculously large.)
If the character reaches the ground they will then need to deal with The Miasma - and any wandering Gargantuan!