Its quite common, You only need to adhere to the resignation date in your contract if you need a reference, otherwise, it is irrelevant.
Having said that, depending on the circumstances, a teacher leaving without proper notice might still get a good reference.
It might not be the teachers choice, it might be the school, is it an NQT who has failed their induction? Is it a redundancy?
If it is a short term or temporary contract, the notice dates do not apply anyway.
If she has been badly treated she will be entitled to leave. if she has a compromise agreement she will be entitled to leave. If she feels the timetable she has been offered for next year is in breach of her contract, she will also be entitled to leave! If the job has made her ill, she is entitled to leave.
Quite apart from that, you still have 8 weeks to fill the vacancy.
One of my colleagues is so angry and upset with the school that she doesn't intent to tell them until September that she is not coming back.
( She doesn't need a reference)
I believe you can sue for breach of contract, but this will cost the school more than they are likely to recoup, especially if she has mitigating circumstances, or a defense.