This would not only lead to interesting definitions of Moon-Moons but would also result in possible threats to future landing missions.
The empirical answer is that there is absolutely no risk of debris reaching a permanently stable orbit. If so, then there would already be a lot of such because of the millions of impacts that the Moon has been subject to in the past.
However, for human missions, the question should not only be about permanently stable orbits but also about orbits that exist for longer than a few years. Maybe someone with more expertise in orbital mechanics can say something about this.