Soon the gene that produced the gain in fitness is present in all surviving members of the species. However, this comes with a loss in genetic diversity. The species' pan-genome is reduced in size. The other genes in the fitter individual(s) might not have been particularly better than those in other individuals, but they get a free ride in the sweep.
Many species can reproduce asexually but also have some form of sex. That is, individuals can clone themselves, but they also have some way of mingling their genes with other members of the species. This might be by sex as practiced by eukaryotes, or some form of horizontal gene transfer as practiced by bacteria. This sex could potentially prevent this loss of genetic diversity. The gene producing the fitness advantage diffuses into the general population.
However, when a selective sweep is occurring, it seems to me there is a huge incentive for a gene to arise in the fitter individuals putting a stop to sexual reproduction or horizontal gene transfer. i.e. under this condition sex, which usually increases the odds of every gene's survival, stops being favourable.
It's a disaster for the species, but the unit of selection is the gene.
Obvious parallels to cultural exchanges, software compatability, etc etc.