Ok, then you have a few things to consider.
Who is tracking them?
This is important to know as it defines the limitations of their ability to search and apprehend someone. If it is an official source such as a government, or AA+ Corporation, then the limits of the search end at the boarders of that Organization. Ares can't go into Seattle after someone who has stolen something, because Ares boarders end at the side walk. (At least officially). The UCAS can't chase the runners into the CAS, as that is an other country; And so are Mega-corps! So no chasing runners into the Aztech Pyramid Shopping Complex.
If it is a criminal organization, well then their boarders end where their influence ends. The Vory are not chasing the Runners deep into Yakuza zones, and so on.
It's because of these boarders and boundaries that Runners exist. They are the deniable assets that are used in these situations, simply because they are not tied to a organization or government - thus no political fallout. (Or, declarations of war!). But that is also their weakness. If something goes South, they are left twisting in the wind.. or at the end of a rope (literally and metaphorically).
Why are they being tracked?
Most Corporations are not going to spend a butt load of money tracking down a runner team for a stolen piece of tech beyond, say, 72 to 96 hours. Simply because the Runners probably have handed it off to their employers by that time, which means they are wasting money AND possible legal retributions just to recover nothing. Of course, if the Runners do something stupid - say kill 300 people during a run, then it may be a point of pride that causes them to be hunted...
Leaving a city or country really isn't that hard... The hard part is when you do get in! Honestly, to end out of the city, you put one foot in front of the other until the city is at your back. Done. There is no huge wall that surrounds the cites (generally).. Nor are there a Wall that separates countries (Unless Trump figures out a way to pay for his wall and build it... Then there will be one). The trick is what happens when you arrive in the new country. As an illegal alien, you basically have NO rights in Shadowrun. For all intents and purposes, you are a non-entity, which means you are (again) a member of the SINless masses scratching a living out of nothing.
Leaving a country and/or a City for a Runner is a big deal! Generally speaking, the Runners contacts are all situated where they work and live, and not outside that zone of influence. Which means they need to reach out to others in that city to help them get situated and make introductions. This is part of the job of a Fixer. Fixers are people with a wide range of contacts, it's their job to "know someone, who knows someone, who knows someone who has that thing for sale where you are going" and to get you in touch with them (For a fee, of course).
From there, a Runner basically has to start all over again. They have to build up their contacts, and acquire a Rep as a good operative. (which means working your way up of the local list of talent, starting with the low paying, high risk shit jobs the locals don't want!)
Of course, there is always the Boarder patrols to make the attempts harder.. and they are not a friendly as they are now. Its not a catch and release on the "correct" side as say it is between Mexico and Texas.. Its more of a "shoot it up and deposit the bloody remains on the other side" thing... So hiring a Coyote (someone who specializes in moving people) is a good option.
As for a "Burned" SIN... Well this can happen many ways. The chief way is that it fails a background check, once it gets flagged at a possible fake, its done for. How this happens and when, is basically down to luck, quality and timing. For the most daily stuff a person does, a low level SIN will work. The Buses just want to know you have a SIN, same with the Soykafe Shoppe.. they don't really care who they are selling to, only that you can pay. Going into areas that only "Real, Important" people should be in (like the Business sector, or the Luxury Home Sector) may scan your SIN a little more carefully to make sure you are the "right" kind of person to come in. And finally, there is are times that it is really important to make sure you are who you say you are... like when getting arrested for a serious crime. Or entering a Country, or that Secure Corp Facility...
This is where your quality of SIN matters... the higher the quality of the SIN, the better the details match
you.... But that doesn't mean you will always gain entry "just because". After all, even if my very REAL SIN says I am a Citizen of the UCAS, it doesn't mean I have the right to enter an Ares restricted complex. (But if my FAKE SIN says I am a Ares Employee... I just might get in - IF it passes the check!). (The CRB has the rules of SINs and checks)
Having a SIN burned, means you throw it away, and every thing that is attached to it, as it has effectively been "frozen" anyway. For this reason alone, many Runners "run" with several SINS. For example look at my main character:
He has a rating 6 SIN that he "lives" under. This contains his home address, his permit for his heavy pistol, his permit to operate a vehicle, and his permit for magic, and that's about it. After all, a Professor of Mystical Theory doesn't need much more then that. Now, since he has used that SIN for a while it has a whole bunch of background data on it (like where he shops, what he eats, and so on) and that's fine, it just adds to the SIN. And it basically allows him to "live" the life of a wageslave... and never gets used for or around anything that even smells illegal. (lets call this one "Bob")
Then he has a Rating 5 SIN that is used for when he has to move about in the City. This one is linked to more equipment that gets used in more "passive-aggressive" situations, and is tied to a cover identity for that purpose (in this case a mystical private investigator) so it allows me to use more specialized tools of the trade without drawing too much attention (this one is called "Fred")
Then I have a Rating 3 SIN. (we shall call "Doug") This gets used when I have to purchase something that I don't want linked to either "Bob" or "Fred", and includes things like weapons, ammo, extra drones, and toys, specialized clothing, ETC....
Since all these SINs are different, and do not connect to each other, they can be burned individually, but not as a group. Meaning that if "Doug" gets burned because the Rating 3 SIN fails in a check VS a rating 4 checker, then ONLY "Doug" is burned.... And the "real" Doug (if there IS a deal Doug!) is getting a visit from the police! (If I am not arrested on the spot!)
Since I only accept Certified Cred for payments from Runs, I can keep my money separate from all 3 identities, and transfer what each SIN needs from Certified Cred as needed, when needed. (Remember Certified Cred is NOT linked to SIN, but stands separate from them all. It is the $20 bill in your pocket.... If you drop it on the ground and someone picks it up, they too can spend it... unlike say your Bank card while is protected by a PIN)
If I
have to accept a SIN transfer of funds. (Say "Bob" did something and got a reward and the money was given to "Bob") I just transfer the cash into Certified Cred at a banking institution.
It should be noted that, sometimes Runners buy or get things that can NEVER be explained away. These are items that have an Availability rating of (F). Sure I can get a permit for my heavy pistol, but I can never EVER get a permit for my APDS ammo I have loaded into the pistol! Nor for that piece of (F) rated Cyberware! Those are items that are strictly, legally speaking, for the Government's use and ownership. (Government being a loose term here, as Ares is the Government for Ares property). So chances are, they never had permits for half their shit anyways
Does that help you out some?