Can be tricky but is doable as long as the school releases you from the contract. I have known a few teachers who got of contracts and then got new positions. I have not known any though who did so in Sept of the school year. I am in a bad contract situation myself at a private college, but I would not break it just yet. I have some concerns about things but I am not in it alone and we will see. I have no plan to get out of the contract but a few times the thought raced through my sleepless mind. In fact I will do the whole year and see what happens. I will just have to adjust but I am not happy really. But not many schools would even consider employing you if you are sill in a contract at a school. It is some big deal here. I have heard there is some black list of foreigners who have broken contracts but I cannot really find proof of this.
It can depend on the school and how you handle it. I understand that once you get out of a contract and you z-visa is cancelled (it will be cancelled) you have about two weeks to get an L-visa that, now, is good for 30 days with no extension. I am not sure and there is so much visa confusion I do not want to add to it.
When I was in Beijing (pre-Olypmics BJ, the good ol' days) the situation seemed to be a little better and there were more options. I definitely have know several foreigners, Americans and Australians, who quit the job I had there who stayed in BJ and worked. On the other hand I have heard of people doing the same in KM and winding up on the "blacklist". There just aren't the same work options here, not even close.
The best option, in my opinion, would be to bite the bullet and wait out the term at least and then make the changes between terms. And to be honest what does unbearable mean and will they find a position that is not unbearable at the next place. It can be like jumping from the frying pan into the fire here sometimes.
The school I was at for 6 years let me and some other teachers go rather suddenly and unprofessionally, to save money basically. It was really sudden and my visa was about to be processed even. I was told, as were they, we were all getting new contracts at the beginning of May. It was not a performance or attitude issue. The school leaders found out the teachers had been working 8 to 10 hours and not the contract's 18 hours. In June they decide they do not need all these pesky, whiny waijiao and let a few go rather coldly and without any real warning. I got a new job within a few days by walking into schools rather than searching on the net. I thought the new gig would be a step up from all I was told, but it is not (I will not name the schools). People have to deal with things here really. What can I really do? I have classes of about 50 non-English majors who are mostly boys. No computers. No pictures on the walls. No chalk most of the time. That is that. Better than the high school I did up in Jilin City with no heat in the middle of winter.
I would say try and give it some time. It is only the first month. Worst case scenario would be she has to quit (on decent terms, not arguments and confrontations), goes back to the US and gets a new job from there if she does not get a release letter. No release letter = no new job. But you can just leave and apply from the outside as though it were your first time. They won't know and I doubt about the existence of blacklists.
I am not sure it would be so easy to get a new job in the time frame she would have to sort out her residence permit and visa issues. She has t be here legally to work and stay out of jail.
In the end in China you either dodge a bullet or you bite it. Sounds like she might be at a high school or middle school? Well, I wish her luck indeed and hope it works out.