The king of the Unicorns.
The Unicorn King first appears in the short story Debt in which Hunter Jusenkyou returns the Sepilcorn to a group of Unicorns, which allows them to revive the king. This allows them to reproduce their species, which they were thitherto unable to do.
The horn of the Unicorn King, physically like any other alicorn, was found in a museum where it was displayed as a false alicorn. Unless it is attached to the Unicorn King, the species cannot reproduce, though they can die. When the horn was in the hands of humans, the souls of the dead joined it; but no new unicorns could be born.
When it was returned and the king restored, new unicorns would be born with the complete memories of the roughly 8,000 years during which unicorns were nearly hunted to extinction.