In short, the target would be prone in the space they moved to and not be able to move any further, effectively ending the Stride action.
From the PF2 SRD (emphasis mine)
Some reactions and free actions are triggered by a creature using an action with the move trait. The most notable example is Attack of Opportunity. Actions with the move trait can trigger reactions or free actions throughout the course of the distance traveled. Each time you exit a square (or move 5 feet if not using a grid) within a creature’s reach, your movement triggers those reactions and free actions (although no more than once per move action for a given reacting creature). If you use a move action but don’t move out of a square, the trigger instead happens at the end of that action or ability.
So, firstly, it's clear from this rule that the trigger occurs after exiting the square moved from, meaning the provoking character will fall prone in the square moved to (note that this is different to 1st edition PF).
Next from the rules for the Prone condition.
The only move actions you can use while you’re prone are Crawl and Stand.
So, even though the target is in the middle of a Stride action, being Prone is now preventing them from using this action. Therefore, the action ends. The target could now use a new action to Crawl or Stand, assuming they have any actions remaining.