What was the crime? Murder, injury, insult, property damage; attempt of any of those.
Was it real, perceived, accidental, erroneous…?
It doesn't needs to be perceived as crime by the Persecutor, but by the Fugitive. A teen has gotten pregnant and rides from home, thinking her father is going to make her abort, the father pursues her, not because he intends to force her one way or the other, but because he loves her.
Upon who was committed the crime?
Upon who is the punishment going to be committed? For the Fugitive to flee, the Persecutor must want to punish the Fugitive, but it may decide after some time that it will take revenge upon others, giving the story a time limit.
Since it flees, it doesn't want to face the Persecutor. This could be because of fear (the Persecutor is more powerful), embarrassment (the Persecutor is the Fugitive's own father, pursuing by duty) or whatever reason.
The Fugitive does not need to know personally who is pursuing, only to believe that somebody is.
PCs as Fugitive
If the PCs are fleeing, you know it because that's what they did the last session. What I mean is that, in a conflict between PCs and NPCs, you never know if the PCs are going to flee or to fight, and often what you can foresee is the fighting, so in last session the PCs found they bit more than they could chew, and chose the best part of valor.
Now you can plan a pursuit story, probably using it for them to look for a conclusion.
The Persecutor is not only pursuing, but probably mixing other plots, like Enigma, to track the Fugitive.
PCs as Persecutor
Besides the PCs needing a reason to pursue the Fugitive, this case doesn't need much more work.
If the Fugitive is caught, the story develops into Vengeance or maybe Supplication if the Fugitive asks the Persecutor for mercy.
The Fugitive may be fleeing to gain time and solve an Enigma, like who was the real culprit, or getting what he needs to definitely escape the Persecutor (Daring Enterprise, Obtaining or Conspiracy).