It's not just a Destiny thing anymore.
Borderlands: The Pre-Sequel players have begun stumbling across incredibly efficient loot/experience/badass rank/moonrock grinding spots (that's my nice way of saying "exploits"), so of course they're calling them loot caves. We live in a post-Loot-Cave world now. Yes, this is the year 2014 AD, but we're starting the count over next year to begin the PLC era.
Two Borderlands "loot caves" are especially prominent. One is part of the mission "Let's Build A Robot Army," and it's totally inaccessible after the mission ends. In the mission you've got to help turrets mow down a bunch of infinitely spawning baddies like sweet, springy space grass, so the keys to keeping the farming spot alive are a) killing enemies before the turrets can and b) quitting out of the mission right before the turrets reach their allotted unfeeling death quota. Deathmule demonstrates that here:
The second so-called "loot cave" is in The Pre-Sequel's final area and is especially ridiculous. It pops up as part of the "Guardian Hunter" mission, wherein your goal is to capture a guardian fire wraith. However, if you're feeling so inclined you can also just kill them infinitely. They respawn very quickly too, so your experience and—if you opt to switch between weapon types—badass rank will skyrocket. Here, JHFLEETING demonstrates the cave and claims it took him from level 27 to 33:
Obviously, both of these "loot caves" eventually outlive their usefulness, but apparently they're good for multiple playthroughs and difficulty levels.
So hurrah. Hurrah for standing in front of things and blindly firing until, suddenly, it's Christmas—in multiple senses of the phrase. No, this won't be the, frankly, inspiring display of silent human cooperation that Destiny's Loot Cave was, but getting glittering piles of stuff is always nice. I'm wondering if 2K will eventually patch these things out, but for now you can farm to your heart's content—you know, if that's your thing.