Of course ours was a low stakes game, but do the official rules say anything about how to deal with this kind of situation?
It's difficult for me to find a specific ITF rule that speaks to this. Basically the rules assume that the ball will always rebound from the racket and specify when you lose the point based on what the ball does hit.
But the player with the ball stuck would lose the point. There has been no equipment failure (the racket didn't fail). There has been no hindrance from the opponent. So it becomes loss of point for failure to properly return the ball.
One example of this happening in an professional event was the 2014 US Open second-round match between Stosur and Kanepi. For the first point of the 9th game in the third set, Stosur serves and manages to wedge the ball in the racket during a return. The point is awarded to Kanepi.