I'd consider an intact culture to be one that's capable of transmitting its knowledge and traditions to the next generation, and one that permits some kind of social learning [1]: It should be possible for a child or novice in the culture to be able to figure out how they are expected to behave, consistent parameters should exist for interactions, etc.
A broken culture in this case would be one which:
- Lacks a next generation/dies out (e.g. the Shakers because of their disdain for sex)
- There is a lack of agreement on foundational rules which make the culture impossible to enter, change, or expand (because the culture is crisis). Think managers giving you completely opposite instructions. One example would be say, attending the religious services of a friend/colleague. If the rules are clear and consistent and conveyed, it's possible to act in a respectful way. "This is how a Catholic wedding works." If you just have to guess what's offensive or what the taboos are, or you get contradicting answers, that's a broken culture. Even insular cultures need to teach children/new members, if they can't, they die.
[1]: https://en.wikipedia.org/wiki/Social_learning_theory