What is the statutory basis for parties being able to agree to modify a final money judgment in California?

CA Code of Civil Procedure section 473 allows a judge to correct mistakes in a judgment or set aside any judment, and section 664.6 allows parties to have judment entered by stipulation, so depending on how much time's gone by and whether the court retained jurisdiction, it might be possible to make a motion based on those combined statutes.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.

If you submit a stipulation to the court modifying the judgment, signed by all parties and counsel, it should be signed and entered by the court.

I would strongly urge you to consult immediately with a litigator skilled in this area of the law.

PLEASE NOTE THAT THIS RESPONSE SHOULD NOT BE CONSTRUED AS A LEGAL OPINION OR ADVISE, AND DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP. IN ORDER TO RENDER A LEGAL OPINION OR ADVISE, THE RESPONDING ATTORNEY WOULD NEED FAR MORE INFORMATION THAN HAS BEEN PROVIDED, AND WOULD NEED TO BE RETAINED PURSUANT TO A WRITTEN FEE AGREEMENT.