Cooking with blood has a long heritage in Europe (especially France), and certainly other areas, as well. Blood sausage or black pudding is basically pig’s blood and fat (and often onions), encased in a length of intestine, and is thought to date to ancient Greece. Sanguette, a dish still prepared in southwestern France, is little more than fried coagulated chicken blood.
Blood, or alternatively puréed liver, adds richness and color to brown sauces. Liver provides substantial thickening, while blood thickens only modestly. And it is finicky. You should add a small amount of your hot sauce to the blood, then incorporate that mixture into the sauce off the heat. Put it back on the burner and heat it gently until it thickens slightly. If you overheat it, it will curdle. Similarly, you cannot reheat it – it will curdle.
If you added liver or foie gras, strain the sauce before serving. You can hold such a sauce briefly before serving, but it is not stable enough to keep for long, and once it curdles, all is lost.