You are absolutely right in assuming that people could and did evade the law during the Roman period: in my answer, I'm going to give you three examples drawing on various kinds of evidence to sketch out some of the ways we can approach and think about these cases.

One group of people that was particularly inclined to abscond and start new lives were slaves: this seems to be something that could happen quite often, especially since there was often no way how to tell whether someone was free or slave. This was partly because there was no racial distinction between the slave population and the free (compared to New World slavery) and because the clothes they wore would be essentially the same as free men and women working the same or similar status jobs would wear. This is also shown by the fact that we often get cases of people who claim to be free whereas others say they are runaway slaves: the boundary between who was a fugitive and who was not was oftentimes very permeable. This is of course generalising and conditions of slaves varied immensely across the Roman world - the ability of a slave working in the mines to escape would be extremely different from a slave herder on large agricultural estates, who could oftentimes spend a lot of time alone outdoors with their herd (and thus Varro is extremely concerned about making sure they have a reason not to run away by for instance giving them slave women as partners - see De Re Rustica, Book II). Different still would be the situation of an urban slave, who accumulated over the course of his life money in his pecunium (private 'purse' or 'pocket money' of a slave) that would allow him or her to move around more smoothly.

Note not all slaves ran away or indeed wanted to, but some did, even if faced with lots of obstacles: and slave-owners were sometimes very anxious about this. Theoretically, as Keith Bradley writes, 'a slave-owner wishing to return apprehended runaways and to punish those who had harboured them was entitled to assistance from provincial governors, civic officials and troops, who together with harbour-masters had powers of arrest and were obliged to guard recaptured runaways': but this would presumably be quite difficult to coordinate in theory, especially since information-sharing was complicated by both the practical difficulties of a large, decentralized empire such as Rome was. In many ways then, slave owners had to go the extra mile, and we can see that through my first example of slave collars. There's a significant amount of them to be found in the Roman world: one, currently in Rome's Palazzo Massime alle Terme, has an inscription that reads: 'I have run away; hold me. When you have brought me back to my master Zoninus, you will receive a gold coin.' We usually assume these collars were given to particularly troublesome slaves in order to hinder their efforts to flee from their masters: they were made of metal and would be quite visible when worn. In some ways, then, Roman justice relied on the willingness of its citizens to participate in something that was seen as in the interest of 'public good' and necessary if the whole system was to function.

But even if one was wealthy, influential and could rely on personal connections in order to 'get things done', his or her slave could be successful in running away: this is my second example, drawn from Cicero's letters. In Fam. 13.77, adressed to the governor of Illyricum, he says the following: 'Once more I beg you with more than common earnestness, in the name of our friendship and your unbroken zeal in my service, to bestow some pains on the following matter also. Dionysius, a slave of mine who had the care of my library, worth a large sum of money, having purloined a large number of books, and thinking that he could not escape punishment, absconded. He is in your province: my friend Marcus Bolanus and many others saw him at Narona; but they believed his assertion that I had given him his freedom. If you would take the trouble to restore this man to me, I can't tell you how much obliged I shall be to you. It is a small matter in itself; yet my vexation is serious. Bolanus will inform you where he is and what can be done. If I recover the man by your means, I shall consider myself to have received a great kindness at your hands.' Dionysius pops up a couple more times in the correspondence: last time we hear about him, in Fam. 5.10a, the governor assures Cicero he hasn't found the runaway librarian yet - we can probably assume he got away, perhaps absconding outside of the empire, in which case it would extremely unlikely for him to be ever returned to his master.

With the final example I want to give you, we'll move from runaway slaves to a more typical 'criminal'. In Richard Alston's book on the 'Soldier and society in Roman Egypt', he argues Roman soldiers often functioned as 'police officers' of some sorts, being tasked with keeping law and order in the surroundings of their posts. Of interest to you is one of the papyri fragments he present in order to make this argument, BGU I 4, in which we learned of an investigation of a case where a veteran deposited his property with a soldier who consequently left the area. We don't know how this case went down, if it was resolved and the thief was found: what it does tell us that this was something people could do and presumably could believe they would get away with it.

Throughout these examples, I have tried to shown you one final thing: it's very hard to approach the people you want to know about. Our sources for Rome are often extremely fragmentary and limited for people below the elite, and we can often only get glimpses of them through chance (the survival of the papyri) without much more context. That being said, I think your question gets absolutely right one thing: the disconnect between what the law said and how it could be enforced. However hard it is to approach these cases, I think this is the one thing that shines through quite clearly.

For introductory reading on slave fugitives, I'd recommend Keith Bradley's article on Resisting slavery in the first volume of The Cambridge World History of Slavery. Richard Alston's book is great for thinking about the role of army in enforcing justice. Knapp's Invisible Romans is accessible to the general audience and has a chapter focusing on evidence for outlaws, pirates and other criminals in the Roman world, which might give you more to think about.