In general, yes. The obligation to pay ongoing child support ends when the child or children in question turn 18 (or whatever age the child support order says), but that doesn't do anything to stop back child support. Thus, if your ex-husband disappeared when your children were 12 and 14, he still owes 4 years on the 14 year-old and 6 years on the 12-year old. Interest and penalties may apply as well.
Do you have a case through your county's Child Support Department? If you do, you may want to tell them where your husband is now and where he is working so that they can go after him. The Child Support Department in your county should also be able to tell you whether your ex-husband owes the support to you or to the state of California. Different rules may apply depending on who is owed the money.
Hope that helps.
The answer provided above is based upon California and/or New York law and is based solely upon the limited information provided by the poster. No attorney-client relationship is created. A future in-person consultation may reveal additional facts that may change the answer provided.