As you return back from the Treasure and walk on the beam, if you jump towards the broken part of the ramp (as the arrow above shows), Lara may grab the edge and hang instead of landing on the ramp.

Although it seems ok, Lara is not able to pull up. So, you do not have another option but to release and fall to your death. However, the last registered Checkpoint is at the entrance of the room, meaning that you have to go for the Treasure again!

To prevent this problem from occurring, avoid jumping towards the ramp. Instead, keep walking on the beam until Lara is actually inside the ramp (as the arrow above shows).

Then press forward to step on the ramp.

If, however, you hang from the ramp, there is still a way to survive from the drop.

First traverse to the middle of the ramp. If you move the Left Analog Stick to the right, Lara will stop in the middle which is where we want her to hang from. (The yellow X's show where you should not hang from.)

Release to land on top of the pillar below. You will not be able to see Lara, because she is inside the V-shaped rock. If you move on the spot, you will be able to see her shadow.

If you attempted to release hanging from the left part of the ramp, Lara would miss the pillar and fall down, ending up dead.

Without turning at all, walk forward (inside the V-shaped rock). You will fall off the pillar and land on the stairs below.

In a different scenario, Lara will fall down, but the baluster of the stairs will cut her momentum, ending on the ground alive.