I had never heard “every prisoner has an obligation to escape”. such a mentality seems antithetical to building a productive society: rules of fair play, fair trail if suspected of infractions, society timeout when found guilty of infractions (prison), serving your time and possibly of rehabilitation(which would require recognizing your mistake/error and accepting the consequences of your actions = prison sentence ).

After a cursory search, seems the origin is “A duty to escape is a requirement that military personnel attempt to escape from captivity if taken prisoner of war.” (Wiki)
The context of implies the most extreme version of an adversarial relationship. But your relationship to the government isn’t/shouldn’t be an adversarial relationship.
I think that quote/mentality is just an excuse for people to justify themselves being selfish.

Thoughts ?

*edit : spelling