When you have a huge stack you can afford to play much more loose than usual, but when you get down to less than let's say 15-10 bbs it kind of becomes a push/fold strategy and at that moment what you actually should do is tighten up your range rather than loosening it because you want to give yourself the biggest
odds of winning the pot, either at showdown or preflop.
Tightening your range at those times will give you an image of a player who has big hole cards and might either make you opponents fold which lets you pick up the pot easy, and if you go to showdown you're gonna be holding something decent in your hands. Basically at that point you're waiting for any broadway suited cards, mid to high pairs, and you shove them as hard as you can.