What happens after your characters (whatever your SF system of choice) break the law? The usual answer is 'we lift ship asap!'
That's a very good strategy but again let's see what happens.
Let's say you break the law and buy a ticket to a planet one parsec away, one not regularly visited by the planet you just cuckolded. That means it will cost that planet's government at three tickets to bring you back for trial (sheriff ships out to get you, sheriff ships you and himself back to original planet for trial). In Cepheus Engine this means 26,000 credits. Why yes you are paying for high passage. No one is going to want to share a cabin with a captured fugitive, though the sheriff can fly middle passage.
Low passage is a distinct possibility (for the prisoner at least). But losing a prisoner to sleeping sickness and then finding out he was innocent (or presumed innocent from the start as some cultures believe) might be regarded as a violation of rights. So you'd probably have to go with high passage for the person of interest.
That 26,000 cr. means some crimes are plain going to be forgotten. Assault, breaking and entering, theft etc. The exact details will vary by world. Capital crimes would probably have a higher reasonable cost associated with them.
I am purposely leaving piracy out of this post. Piracy falls under the Navy's aegis. They have plenty of bucks, have to spend their budget and are happy to chase you to the Galactic Rim and points beyond.
Even if it is a matter of murder say, how far will a planet pursue a fleeing suspect? Was the victim anyone important? Are there extradition treaties with his probable destination. Are there other suspects and how likely is this person to be convicted if he is brought back? You can't put a price tag on justice but that's what people do.
If you have communication limited to actual travel it gets even harder. In Cepheus Engine terms you would need at least a Jump 3 ship to outpace the faster civilian ships which means a bottom tier warship in most settings is zipping around dropping off wanted posters. Make that several ships, just to circulate wanted posters. But what then? Are the police of other planets or starport security going to concern themselves with your case? Probably not unless there is also a (fat) reward included. And transportation guaranteed.
Enter the bounty hunter.
Bounty hunters hang around starports and wait for those wanted posters to come in. they read them with great interest. A starport has no laws against packing heavy firepower and they usually do so. They snoop around and buy a lot of drinks and if they play their cards right, they catch a fugitive. What then?
Some planets have extradition procedures with their neighbors. If the crime doesn't warrant the cost of a passage back, then Planet A could try the fugitive under the laws of the Planet B and impose punishment under that planet's penal code. In exchange the Planet B will treat felons from Planet A it captures similarly.
Sometimes a felon will jump bail or be found guilty and still escape imprisonment. In this case Planet A would imprison the fugitive to serve time there.
There are some people, however, that Planet A would want no part of no matter how buddy buddy they are with Planet B. There are some people Planet B wants back. In that case a subsidized merchant comes in handy. Subsidized merchants get funding from the government to provide necessary commerce to worlds. While sending a warship to transport a prisoner is pretty expensive a subsidized merchant could be pressed into service. The Navy pays part of the ticket(s) to transport, Planet B pays the rest. Everyone is happy (except the crew that have a dangerous criminal onboard.
Detached service couriers are great for this. They can be called back to service for almost any reason and a prisoner run is one of those. They usually fit the cargo hold out for the prisoner (meaning a mat and several buckets) and lock the door. With no mortgage and fuel provided by servce bases or skimmed for free they can easily cut costs on transportation. Besides those guys seem to enjoy that sort of thing.
Some couriers even adopted a business model, transferring crooks between the planets of a cluster. From there it's a small step to turning bounty hunter and bringing the bad guys in themselves. A reward is a reward after all.