We have no idea. The common thought is that Belthasar provided for a clean ending somehow. The problem is amplified by the ambiguity of the ending in general, like the entire Schala / Kid thing. We just have no idea, as this Kid is obviously not the one Serge meets, as Lucca on Opassa Beach states that Kid has yet to do it on the linear timeline.
If it weren't for Lucca, there'd be a good way of making a case that they're the same person. But no, we have no idea what happened to the first Kid, and whether the Kid Serge knows would be subject to Time Bastard. I began worrying about the practical limits of Time Bastard, but really, Melchior and Janus's disappearing in Chrono Trigger makes a solid case for the law of conservation of time. So we don't know, and we're left with the reassuring touch that Belthasar at least had a plan. Divining it is another matter.
