What is the name of caramelized sugar dissolved in vinegar used to flavor sauces?

That's a great question! There isn't a specific name for caramelized sugar dissolved in vinegar used to flavor sauces. You can call it a caramel glaze, caramel reduction, sweet vinegar sauce, or simply caramelized sugar vinegar.

The key is to convey the caramelized sugar and vinegar elements. You could also use descriptive terms like "deeply savory" or "complex and sweet."

Ultimately, the best way to describe it depends on the specific context and how you want to present it.