In New York, if the marriage does not take place the person who gave the
ring is entitled to have it returned.
If the marriage has occurred then the ring is the property of the person
who received it.
The basic law is that the ring is a gift given in contemplation of marriage
and therefore once the marriage exists the ring is a gift that has been
received in "consideration" of the marriage.
The exception is that if the person who gave the ring was not divorced
when the ring was given and the marriage does not take place the ring
does not have to be returned. The reason is that the person, at the time
that the ring was given, did not have the legal capacity to become engaged
because the person was still married. Therefore, it is treated as a gift
without any condition.