It would sound more natural to say "The prison is overcrowded." However, "The prisoners are overcrowded" is easy to understand too. "Overcrowd" as verb can be used with people "They overcrowded the elevator." So I suppose the past participle can be used with people as well. But again, it's more commonly used to refer to places and situations.

perhaps the sentence went like "the prisoners were overcrowding the cafeteria" "the prisoners are overcrowded" does sound strange as overcrowding refers to places where there are excessive number of entities. as prisoners are multiple individuals and not a place or space, it is probably incorrect to use it like that. well unless we are talking about spirits or emotions like "the prisoners are overcrowded with agony and spirits of their victims" where the pretense is someone overcrowding the prisoners with spirits by magic or words that inflict agony.

You could say the "prisoners are crowded." I agree, "overcrowded prisoners" sounds strange. Both people or places/spaces can be crowded. Only places/spaces are usually overcrowded. An overcrowded person sounds like a person is a container for other people. Maybe you could say, "A person with multiple personality disorder is overcrowded."

No, you cannot say "the prisoners are overcrowded". However, you can say "the prisoners are overcrowding the place" or "the prison is overcrowded".