This is actually terrifying in many respects. It's the basis of the eternal return idea, probably best known from Nietzsche, but found in many traditions. It compounds the consequences of anything that ever happens. Without it, you can at least take comfort in knowing anyone with the misfortune to live and die under chattel slavery, Naziism, or some other great evil at least only had to do it for one lifetime and then they get to escape forever to eternal peace. In a cyclic infinite monkey universe, nope, everything that ever happens happens infinitely many times, and those people who spent their entire lives on a plantation in fact spend eternity on a plantation. It's hell but real, and not levied as punishment but by pure randomness.
Except they're not the same person, they're just (mostly) variations on people that happen to be similar. It's a big universe. If it proves to be even more staggeringly big, well, it's more than I can comprehend either way.