I have read that among wild equids, fillies may be run out of the herd as well as the colts, as they reach sexual maturity. Fillies have no trouble finding a new herd or stallion. Colts of course form bachelor herds, until one feels bold enough to challenge and best the local herd stallion. If he wins, he may well end up breeding his own mother and half-sisters. I don’t think they know or care.
Of course, when you’re talking about wild animals, and the risks inherent to non-adaptive recessives cropping up in the offspring of inbreedings…well, nature isn’t very forgiving. If such offspring occur, and the recessive trait is nonadaptive, they’re not likely to survive infancy, let along grow up old enough to reproduce themselves. So in animals, it’s probably less a problem than you’d think. In humans, where we tend to try to save and care for people regardless of their genetic damage or physical handicap, and who may well grow to adulthood and even reproduce, I’d say it can be a problem. And I have heard of some real problems in isolated/heavily intermarried regions or social groups, like the Amish, and some isolated villages in 3rd world countries.
But I think - and I know I’m getting way off the OP here - that the survival of such individuals is due solely to the compassion of other humans. It could not happen in the animal kingdom. Nature weeds out the unfit (and a lot of the fit); so inbreeding is not a problem.
Now my caveat: if a breeding population becomes too small, as is true with some of the severely endangered species…great care is necessary to keep the genetic base as broad as possible. Caretakers of the species are very careful to keep records of who sired whom, and how closely related to which, to avoid inbreeding and the production of unfit individuals, which might be conserved when they should be excluded from the gene pool.