So who actually broke it off? If the woman does then perhaps she should give it back. If the bloke did then she shouldnt.
In the end its a bit of jewellery, if she gave it back you sold it, bought something else and gave that to woman 2 you would still have two rings in circulation although one now belongs to someone else. Effectively you are using the same money to buy the second ring so it is the same ring.
No cause Id use the money from the first ring to go out and get hammered
the money would be long gone, its not like Id be working a chain of women.