Technically, a spouse who moves to another country is still supposed to pay child support. Legally, though, it can be very hard to get him or her to pay. The reason is that many countries do not have standing laws and agreements saying they'll help if a spouse flees over the border to avoid payments.
There are officially 195 countries in the world. Just 15 of them have agreements with the United States regarding the enforcement of child support. There countries are Australia, the Czech Republic, Canada, El Salvador, Hungary, Finland, Ireland, Northern Ireland, the Netherlands, Poland, Norway, Portugal, The United Kingdom, the Slovak Republic and Switzerland.
As you can see from that list, it leaves those who do not want to pay with many options. One woman, who is a single mother and who must care for two children with special needs, said that she was having a lot of trouble providing that care because the father of those children simply split for Mexico when he was told that he had to pay. Mexico doesn't have any standing agreements with the United States.
This doesn't mean there is nothing you can do, especially if your spouse comes back to the United States after not paying. There are still options and your spouse is still expected to follow the court order. However, the above information is very important because it shows how crucial it is for you to know exactly what legal steps you need to take. Be sure you gather all of the information you need if your spouse is trying to use foreign borders to keep from paying in California.
Source: NewsMax, "Deadbeat Dads Enjoy Immunity from U.S. Laws," Dave Eberhart, accessed April 18, 2016