Exactly. The king sends Crono to the South (Porre) to acquire information on why there seems to be less and less communication between the 2. There, he learns of a special mission (via a soldier in the hospital) that has been going on for quite a time. What that is he doesn't know, but Marle suggests going to find "this Alex" and spy on him essentially.
Last the soldier heard, Alex and troops entered the Forbidden Forest about 3 months ago, but they have yet to hear from him. This is when the Forbidden Forest becomes (unlocked) and you get to go on that quest.
And EVENTUALLY, Crono comes to the area with the cave (The Cave of the Hijira) or whatever you want to call it.
They enter and find your deranged monster inside. I'm thinking only magic attacks will hurt the thing and physical attacks do VERY minor damage. Which would explain why the soldiers got their butts handed to them.
After battle and upon viewing the mangled soldiers, he finds Alex, barely alive outside. Either that or the slave comes and takes him away while revealing a bit of this mission. Which reminds me, should Crono or Therris should save Alex? Let me know.
In any case, that's what I have up to now. I have yet to work much more on Alex's quest, as it happens after Crono's is "completed" (in other words what I have so far). So, I'm unsure on how you want to proceed after he wakes up in the hospital. Let me know because right now, I gotta get ready and get to work and such. I'll read and update more later on.