If Neanderthals and Sapiens were separate species

[Warpy]

8. Female offspring are sometimes fertile

which is how we get things like designer wild/domestic cat hybrids. The fertility rate isn't 100% for females, which is why we have such a low percentage of Neandertal DNA in modern humans outside Africa. The farther apart the species are, the lower the female fertility rate.

We were very close to Neandertals, about 95%. Fertility among female hybrids was likely common, while males shot blanks. Some studies have suggested an early disappearance of the Neandertal Y chromosome fairly soon after contact, but that hasn't been conclusively proven. Studies have also suggested Neandertal populations had declined to a point inbreeding was beoming a problem by the time we left Africa, but that hasn't been conclusively proven. All we know for sure is that part of that species lives on in us, that we didn't simply see them and slaughter them like people thought we did 50 years ago.

(I'd love to see a friendly domestic cat with the Pallas cat coat and range of facial expressions, but alas, the divergence was too long ago and they're most likely incompatible)