I have a Canadian friend who is currently married to a Chinese citizen. She's contemplating a divorce.
Would that action then result in cancellation of her marriage residence permit?

I think you are correct, but contact LongDragon, posts on here, a Chinese lawyer.

If she is going to get divorced, I believe that she can start the process in the Canadian courts. Once the process has begun, her partner cannot file for divorce here.
That means that any settlement will be on more favorable terms for her.

However, if she can prove he has been adulterous, that is against Chinese law, and I think she can claim everything.

Yeah, she can prove he has been adulterous, but I think they agreed to part on friendly terms.

At this time her primary concern is the residence permit.

Most likely the residence permit won't be cancelled as a divorce court won't communicate with other government offices unless the husband asks that they do.

So the residence permit won't be cancelled unless the husband asks for that.

Even if the husband does not cancel the permit when the divorce happens she won't be able to renew it.

My friend has to renew his marriage visa every 2 years. Not sure how about your friend, but if its a same case then as Yuantongsi says "won't be able to renew it".