Rule is once you give it to her, its hers. If the engagement is broken before there was a marriage, the guy when he cools off ultimately realizes he got off cheap and was very lucky at that. Fagettabawt the ring.
If he refuses to pay for it the creditors can sue both him and her since she has an item not paid for and I wonder what the IRS might say about her getting such an asset in terms of income(since the wedding is off) without paying a “gift tax” on it? It might be worth an audit...anyway.