What is a State without Democracy, or Vice Versa?

The reason you can't have a constitution without a democracy is that you can't be a state without people in it. That's why democracy is required for nationhood. Republican status isn't required for nationhood, a country's laws could have been made by an aristocracy and passed down generations temporally by a line of monarchs. The existence of a national state requires at very least that there be people acting in concert. The law itself can, in practice, exist both without people (light obeys the law, and was created fully five days before humans). People also can and do exist without following the law, it's considered a state of anarchy.