Legally, the technical term whereby one party could sue for damages over a broken engagement, was covered under the civil offence of "breach of promise" which is to with the fact that a contract has been made and broken between two people. I think it is still technically possible to sue for this today, but I imagine the courts would throw it out.

I briefly studied a case from the 16th century as part of my University degree. I am sure cases occured during JA's time, right up until Victorian times, but the thing to bear in mind is how rare they would have been - its not exactly cheap to go to court - you would have had to be pretty rich / sure you were going to win to make it worth it.