You need to provide more information before this question can be answered. If the apartment were rent stabilized and you were charging your subtenant an amount exceeding the legally registered rent for the apartment, then the subtenant would have a potential claim against you for a rent overcharge. Such a claim would allow the tenant to recover the amount charged in excess of the legal rent. That award could potentially be trebled.
If the apartment is a condo or coop, there may also be some sort of restriction on the amount you can charge a subtenant. Charging the subtenant more than the allowable rent in these circumstances is a breach of the condo or coop bylaws but does not give the subtenant an overcharge claim against the tenant.
None of the situations above, however, would entitle your subtenant to recover all of the rent he has ever paid you.
You should consult an attorney concerning this matter.
He can sue but he won't win. There are no provisions in NY law for a tenant to recover past rent.
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I don't necessarily fully agree with all the answers previously provided and I believe there are some limited instances under NY law where a tenant could actually sue you to recover rent that he previously paid - but in all fairness to my colleagues your question is not very clear.
Before I even ask you for clarification, can you tell us why the tenant has threatened to sue you? I wonder if it's perhaps something unrelated to the rent increase.
My answer is for general purposes only and is not not intended to establish an attorney-client relationship, nor is it advice upon which you should act or rely. But, if you really want me to tell you something upon which you can actually rely: don't eat yellow snow.