Archaeology provides some evidence that these prisoners were not forgotten about. The oubliettes at the Château de Pierrefonds and Château de Chinon in France for example feature stone beds, pit latrines and a hole in the ceiling used to descend food with a rope, which indicates that the prisoners were kept alive.

The notion that prisoners were forgotten seems to stem from a confusion between actual oubliettes and storage rooms where animal bone remains were found, and which did not feature any of the equipment I mentioned above.

Another fact to support the claim that prisoners were not left there to die is the relatively small number of oubliettes in most castles. If you only have a few cells, it means you keep them for important prisoners (to ransom them for example), ones that become useless if you kill them.

Source : Viollet-le-Duc, Dictionnaire raisonné de l’architecture française du XIe au XVIe siècle - Tome 6, 1868. (quite old but still used in academia, at least here in France).