Look at how many people get caught trying to cross the border after they commit a crime. They don't care about the future, just getting away from the police. It can take years to extradite someone.
Plus they aren't immigrating. Their just trying to hide out until they can move on.
What do they do for money for food and a job?
Perhaps extraditing a criminal with a fancy lawyer and a ton of money takes time. But someone with no income? How do they live?