I am divorced and receive a small alimony payment. I f I live with my boyfriend, can my ex stop paying?
If it turns out to be a supportive relationship (financially), then yes.
It would depend on the language in the Final Judgment. If it states that you can not cohabitate with another person or you will lose the alimony payment, then your ex would be within his legal rights to stop paying, after going through the proper legal steps.
In Florida if the court determines it to be a "supportive relationship" then your ex may be able to stop paying alimony. However he would have to file a Petition and hearing would be held on the matter.