Thank you for your question.
When parties purchase property jointly, whether engaged or not, they both have an ownership interest in the property and rights to possession. The difficulty when the parties are not married is that the family courts
have no jurisdiction over the division of that property. The civil court, however, does.
When parties wish to divided their interests in jointly owned property, they may file a partition action per their state's laws. In a partition action, the court essentially determines the parties' rights to the property, and typically orders the property sold and the proceeds divided equitably.
Alternately, if there is a contract between the parties, the court may be able to resolve the issue of a breach. An engagement can be considered a type of contract, but it must be clear to the court that it was the agreement of both parties that the property would be titled jointly in consideration of marriage. If that was the express agreement, it is possible that a court would consider the broken engagement
a breach for which you are entitled to damages, including perhaps title and possession to the property.
This would be a difficult civil case to prevail on, and you most certainly should consult a local attorney if you are interested in pursuing something legally. Here is a link to local attorney directories
I hope this answers your question. Please let me know if you have any follow-up questions.