New Zealand Law
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That is definitely a breach and you could claim damages in the High Court if they try to do this. You must be given a formal notice outlining the breach by failing to pay, if that is what they allege. You can also apply before the due date in their email for protection and an injunction and costs
Eviction may be an opportunity to solve the problem, but you could repond by saying the payments are up to date. Then see what they do. If they proceed to evict with that information you could claim damages for a breach for wrongful eviction at that point.
It could be open to say that this suited you to quit early and you therefore suffered no damages