PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't 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.
It depends. Is there already an order for child support? If so, the order remains in effect until modified regardless of the income situation. If he has an order in place, he needs to get the paperwork going to file for a modification as fast as possible because any change can only go back to the date of filing (Family Code 3653). When he gets to court however, the court might "impute" an income to him. You see, the Judge/Commissioner has discretion to use your boyfriend's "earning capacity" instead of his actual income for the child support calculations(especially if he voluntarily quit his last job).
If there is no order for support, but his ex is trying to get one, it is in the hands of the Judge/Commissioner. Some will put the child support order at zero and require your ex to do job searches. Some will impute impute minimum wage to your boyfriend, unless he is disabled (and can prove it). Some will look to past employment history and impute based on his past earnings, although that happens less these days due to the economy.
The one thing he should not do is just not pay. He will be subject to a contempt citation which can carry a jail sentence (Code of Civil Procedure 1218). If your boyfriend can show he has been diligently looking for work and filed papers for a modification, it could be a defense to the contempt citation. Also, if your boyfriend case a case open with Child Support Services, he should let his case manager know he is unemployed. They might be willing to file the modification for him, or they might refer him to the Family Law Facilitator for assistance. Either way, if they know he is addressing the issue and is trying to get employed, it may help delay a contempt citation. And if he doesn't get a modification, the old order will continue to add up, with statutory interest, and that can get really overwhelming. Urge your boyfriend to get on top of this right away.