Genes code for all the differnet protein molecules in your body; if any of them are damaged, they don't produce that particular protein and your body is all messed up.
This is bad. Luckily, you have two strands of DNA, one from either parent - and a copy of each gene on either strand. If the copy of the gene you need on strand A is broken, no problem, you just use the copy from strand B (or vice-versa).
However, this relies on both strands having all their broken bits in different places.
Think of a slice of swiss cheese - if you need 100% cheese cover on your sandwich, and you have two randomly-selected pieces of swiss cheese, all the holes are going to be in different places, and you'll probably be fine. Maybe there'll be a couple of tiny gaps, but you'll probably get by.
However, if both slices come from right next to each other n the same block, then most if not all the holes are going to line up with each other, and you are fucked.
Cloning creates identical people with identical DNA. Identical DNA, identical defects, repeated over and over through the colony of twins, triplets, etc…
But it’s a small margin of improvement. Both cases, if the population pool is too small, you’ll eventually end up with sterility, severe mutations, and very early deaths, end of colony within a few generations.
If we had a massive population decline, yet, we did not have a global infrastructure collapse (so, magic instant death) then I believe some of the survivors would pretty quickly realize they need yo go find the cold storage of tons of semen samples.
If the total population of a species falls below a certain threshold, that species is doomed due to low genetic diversity.
One last-ditch attempt would be to interbreed with a closely-related species, so the best (as in, has a .001% chance of working) option in this case might be to locate a willing chimp.
It would delay them I guess, but unless you plan to clone everyone forever, it wouldn't be a longterm fix. The genepool wouldn't get any bigger, so once your population did breed, you'd have the same problem.