I don't mean DNA here, just genealogical descent. If two groups of people keep interbreeding, soon everyone has ancestors from both groups. If having even one ancestor from the 'souled' group means you have a soul, that means everyone has a soul after not too many generations. (How many generations depends on how large the populations are and how isolated different subgroups are. But unless there are completely isolated populations, everyone gets a soul this way.) This is the case even if you inherit zero DNA from that souled ancestor.
Mind you, I don't think this idea of physically inheriting a soul (even if not inheriting DNA) makes a lot of sense, but there are those who propose it.