Eligible for continuing CA SDI when residing in another state?

I don't know of any state that provides disability payments -- or any kind of public assistance -- to people who don't live in that state.  The person might be able to qualify for similar benefits in his or her new state, but they would have to apply for them and get approved all over again, and there might be a waiting period.

Please don't think about trying to pretend you're still living in California, when you aren't, so you can still get benefits from California.  It's called fraud.  Sooner or later, you'll get caught, and you'll be facing a large fine and quite possibly jail time -- on top of having to repay all the money you shouldn't have gotten.