The concept of unsatisfied hydrogen bond

"Unsatisfied hydrogen bond" is a bit of a misnomer. An unsatisfied hydrogen bond is actually the absence of a hydrogen bond. You can think of it being shorthand for "an atom which has the potential to make a hydrogen bond, but is unsatisfied in its potential to make a hydrogen bond."

The energy of making/breaking a single hydrogen bond is about the same as the total free energy change of folding a protein. As such, an atom which can make a hydrogen bond in the unfolded state is only very rarely seen not to also be making a hydrogen bond in the folded state. The presence of potential hydrogen bonding atoms which aren't making hydrogen bonds indicates possible issues with that protein model.

However, due to the use of an implicit solvation model in Rosetta modeling, it's often rather hard to make a definitive call about whether or not an atom is making a hydrogen bond. Hydrogen bonds to other atoms in the protein are somewhat easy to see, but there's also the potential to make hydrogen bonds to (implicit) water molecules. Counting unsatisfied hydrogen bonds thus becomes a bit of an art, as you have to take into consideration the solvent exposure (or burial) of the potentially hydrogen bonding atoms. Atoms which are solvent exposed are likely making hydrogen bonds to water molecules.

This is why the count of buried unsatisfied hydrogen bonders is often somewhat flexible. Prohibiting any unsatisfied hydrogen bonders is too stringent, given the inaccuracies in counting atom burial. So typically with Rosetta we try to minimize the number of buried unsatisfied hydrogen bonders, but aren't too concerned if there's a handful of them. (The precise number often depends on the exact structure you're modeling.)