If the beliot in the utensil were from permitted foods, like kosher meat, then hagala is always enough to remove the beliot. This works even by beliot that were absorbed through direct heat because the beliot are not yet forbidden, so one merely needs to weaken them enough that they cannot become prohibited later on. Therefore, even though beliot from direct heat are only weakened by hagala and not removed completely, the hagala is enough to permit the pot to be used again.
For example, if a pot has beliot of meat from roasting and one needs it for dairy (in a case when it is permitted to switch from one to the other), if the beliot of meat are weak then even when they mix with dairy they would not become forbidden (see: Nat Bar Nat). So if one does hagala and weakens the meat beliot, when they subsequently cook milk in the pot, the weakened beliot of meat do not make the milk forbidden. However, by beliot of prohibited foods, even once they are weakened they still retain their prohibited status. Therefore, libun is required in situations when the beliot came from prohibited foods and were absorbed through direct contact, without a liquid medium (such as roasting or baking).
If the beliot of the forbidden food came through liquid, one would be able to use hagala, provided the utensil was first an eino ben yomo (not used in the past twenty-four hours), because of the rule of k’bolo kach polto. The beliot need to be eino ben yomo so that they shouldn’t make the water used in the hagala forbidden, which would then put beliot of the forbidden water back into the utensil.