Guys, we already know what happened. Crono and Marle were away during the Battle of Guardia and went off into the Dreamtime to explore all the worlds impacted by the fires of creation (or whatever it was; it's been a long time since I played Crimson Echoes).
Just kidding. We know that's fan theory and not canon.
The only caveat that we have for the group's survival is that in the anime opening of Chrono Trigger, Crono has a picture of the entire CT crew. He picks it up (we only see his arms, but the armbands match, so I at least assume it's Crono) and looks at the picture, which seems to be reminiscing.
Then, in Chrono Cross, we see the burning orphanage (when did that take place? 1010AD?), and Kid and the other orphan kids had drawn all of the heroes (minus Magus), these pictures taped to the walls.
Based on this, I do feel like kid and these orphans had some contact with Crono and Marle, even possibly the other party members. I'd like to think that the boundaries of space-time didn't stop them, even if the "most canon" ending indicates that everyone must return to their time once and for all (via the telepod gate). Maybe it's the optimist in me.
I went back and watched the anime cutscenes just now, and I definitely wouldn't mind seeing a story that has an elderly Crono, isolated and living in some cliffside cabin atop a cape
overlooking the sea. He meets a new generation of heroes and he'd resolve to train them and help them out, and maybe even join their party. Perhaps even help them alter time so that another version of him can have a better life. Star Trek did that many times and I could see it working here. A Crono that lost everything he loves in the Fall of Guardia and longs for another chance.
EDIT: Which, I just realized, is much happier version of Luke Skywalker in TFJ.