How does the bottleneck effect..?

the bottleneck effect happens when a population hits a critically low point of individuals. because of that, inbreeding levels get high because there's less mates to choose from. when you mate with someone from your family the traits that would not be selected for suddenly appear. so, now not only does the population get small, but also alleles that would be produce healthy individuals produce sick ones. for example, the cheetah populations are suffering a major bottleneck. lets say a disease is recessive in one of the families, it's not even shown because it lies dormant. when two individuals from the same family mate, and then their offspring mate, the probability of more sick individuals drastically rises. alleles don't get eliminated, they start showing recessive traits more often.