Starfleet didn't believe them, or refused to accept such claims.
try it some time.
"I'm sorry orficer, but I'hmm allowed to drunk, drink drive because I renocced my citizenship... CC this to the IRS for me, I'm sure they'll be fine with that."
(If an illegal alien is caught drink driving, are they jailed or deported? or jailed then deported?)
Starfleet could only hunt them in federation space (maybe open space? but they should only be allowed to manhandle their own citizens in open space and even then they're have to be on a federation owned vessel that constituted federation soil, which is all of them if you believe that they are communists sharing a collective wealth. Trying to enforce their laws in unclaimed space on non federation citizens, it's warlordy pirate conduct.).
Only the Federation/Cardassian treaty kept the demilitarized zone safe from Cardassian interference (or Starfleet.) but the Cardassians were getting very tired of this and were threatening to execute them all, if the Federaiton didn't handle this issue on their own side of the border so that it didn't keep spilling over into the Union.