Can the Half-Orc’s relentless endurance protect them from things that would normally kill someone instantly

In our campaign, we have a Half-Orc Barbarian. Very original. We are going along this cliff-side fortress and our worried about falling off. The Half-Orc’s player jokingly says that he’ll be fine, due to his Relentless Endurance. But I was thinking about it, and it seems like he’s right, but this seems excessive. Could he really survive the fall? Or survive lava? Or anything else that should kill instantly?