Legal Question in Family Law in California

It would depend on the terms of the support order or decree that establishes when support terminates.

California Family Code section 4323 provides for a rebuttable presumption of a reduced need for spousal support if the supported spouse cohabitates with a person of the opposite sex. Rebuttable presumption means that your ex doesn't have to prove it reduces your need for support, which would be the normal burden of proof, all he has to do is put into evidence that you are living with your boyfriend. But you still have the right to then prove that your boyfriend doesn't contribute anything and therefore your need for support is not reduced. Of course some spousal support orders terminate jurisdiction to modify support. So if you have one of those orders, then nothing else matters.