Introgression
Genes moving from one population into another and staying there, carried in by hybrids that go on to breed back with the parent population.
A single hybrid is an event. Introgression is what happens when that hybrid breeds back into one of the parent populations, and its descendants do too, until domestic genes are circulating in a wild population that still looks wild. It is slower and harder to see than hybridisation, and it is the reason conservationists talk about genetic integrity rather than just population counts.
It runs in both directions and it is not always damaging: some introgressed genes are neutral, and a few are useful. But for a small, isolated wild population it can erase the distinctiveness that made the population worth protecting, without anyone observing a single obvious hybrid.