Pretty straightforward yes answer, here is a comment by /u/Rittermeister on the subject.

The short answer is yes. The longer answer is it's complicated and they didn't in exist in any way that you would recognize.
There are a lot of different aspects of medieval culture at play here including economics and technology that affected if someone could go off and live in the woods by themselves and thus escape the feudal system. But in order to address the question as a whole we'll have to address each of these in part.
First off feudalism isn't a term favored by modern historians for a variety of reasons. In short, by trying to describe all political systems in Europe in the medieval period, it is by necessity too vague and broad to be useful. Feudalism is at its heart a system where one person pleads fealty to someone above them, perhaps a knight, and gives some of their resources in exchange for other services. Theoretically this pattern continues, with each party pledging fealty to someone above them, but it quickly gets messy, with kings nominally beneath other kings and individuals sworn to multiple lords. Instead, I’ll be discussing polities, ie groups of people, which could be centered around a manor, a guild, a monastery, or a city. Polities are incredibly important in the late medieval world because the government was so localized. If someone was a member of a polity, they had a place in society and had all the associated advantages. These included, but weren’t limited to, access to community resources, protection from violence from outsiders, and legal protection against outsiders and other members of the polity. Serfs are just one member of many medieval polities, and even though we often view them as the lowest, they had access to what I’ve described.

Freemen describe medieval people who were “free”, though as other commenters have said this could mean a variety of things depending on the circumstances. Generally though, freemen were able to rent or purchase land. However, they would likely not choose to purchase land in the forest because they would not be as closely associated with a polity, and thus would not have access to the community resources or the protections that the polity provides. Additionally, the forest was seen as a community resource that was owned by a lord or even the king, so any clearing and selling of forest land would only be done, legally, through interactions with a lord. If the lord wanted to clear forest land, it would likely be to extend the edges of the cultivated land they controlled, ie, at the forest’s edge. This newly cultivatable land could then be sold or rented to freemen as the lord saw fit.

While a lord might sell land in the middle of the forest for a town or village, established through legal charters, there are technological reasons why a lord would not be likely to sell a plot of land in the middle of the forest to a single individual. First and foremost, even if a lord had legal jurisdiction over a forest (which in many cases they did not, because it was owned by the king) clearing land was not an easy thing to do. In fact, it was so difficult that combined with a surge in agricultural yields in the 13th century due to the little optimum, there was a land shortage in Western Europe prior to the Black Death. People couldn’t legally clear land fast enough to keep up with the birth rate.

Another really important thing to consider is how the land was cultivated. The yoked ox was the most common plowing method (for a bunch of complex reasons). Because yoked oxen are difficult to turn, Europe turned into a patchwork of towns surrounded by long, narrow, straight fields, to reduce the turns a yoked ox would make. Oxen were generally communally owned, and therefore if a freeman was attached to a polity, they would have access to a cheap and effective plow engine.

Improvements to the horse yoke during the end of the first millennium CE allowed horses to be a viable draft animal for the first time, but they were more expensive than oxen. They could plow smaller fields though, so if we are looking for a single farmer in the forest, they would have to own a team of horses. Within these parameters, we see that the people most likely to cultivate a patch of forest land in the center of the forest are the people we would expect to, ie the very wealthy who could afford to hire people to clear the land and could afford the more expensive draft animals, or polities of people working communally to clear the land who owned their draft animals collectively. We do not, alas, see a single farming family.
This isn’t to say that nobody was living in the forest. As I said earlier, forests were seen as a community resource and it would make sense then that somebody needed to manage this resource. Enter the foresters, people who would live in the forest and maintain it, making sure that the resources were effectively used and keeping an eye for poachers, similar to a forest ranger now. Foresters are explicitly not “free” from the feudal society, as they are hired or assigned by the owner of the forest (which could be a lord or a polity, such as a monastery). Foresters might be freemen.

Another group of people who lived in the forest were specialist workers who had legal charters to obtain resources from the forest. These would be timbermen or charcoal burners. They would, generally, work in groups for protection and they would not be cultivating the land. They might be the first wave of people sent to clear the land, at the behest of a polity or lord, to make land that would later be rented or sold as arable land.
Other people in the forest might be those who a polity wanted to keep by, but who for a variety of cultural reasons didn’t want living within the city walls. These would be specialists in the polity who performed culturally “unclean” tasks, such as a executioner. While they might have a patch of land, which they might even own, within the forest, they were nonetheless near to a larger polity and were thus connected into the larger web of society. They also first and foremost were not farmers, but specialists within a community.

The last group of people who legally lived in the forest were clergy. Generally though, if clergy lived in the forest, they would do so in their own community, which might in time rise up to become a polity in its own right, including renting the land it owned to freemen. Its a far cry from the self sufficient farmer, but it bears mentioning.
The largest group of people who lived in the forest was undoubtedly the outlaws. Being an outlaw didn’t necessarily mean that an individual was a criminal, rather, it meant that they lived outside the law. In a time of localized government, these were people who were not attached to a polity and were therefore not afforded the legal protections associated with being a member of society. This might be a punishment for a crime, or it could be a choice someone made. Once someone was in this circumstance it became very difficult to be restored to a position of safety within a polity. Without access to community resources, outlaws would struggle to clear or cultivate land, and would often be forced to survive by stealing, or poaching (which was stealing game that rightfully belonged to the owner of the forest). As these infractions build, it quickly becomes apparent how difficult it would be to reform from a life as an outlaw.

So yes, people could go off in the forest and live without being made a serf of a lord of king. They likely could do this because like the foresters, timbermen, or executioners, they were already attached to a polity in a specified manner. The people who lived in a forest or other difficult region, who owned no allegiance to any polity, were outlaws, and while they might do as they pleased, they had not legal recourse against other people. This is to say, outlaws could be stolen from, raped, or murdered, and they and their friends would have no legal recourse. It was not a life many would choose.
Because so few people lived alone in the forest during this period, there is very little available that discusses this subject in depth. For a primer on life in a small polity, I would recommend:
Life in a Medieval Village, by Frances and Joseph Gies
For information on the technological constraints of living on ones own during this period, I would recommend:
Cathedral, Forge, and Waterwhell: Technology and Invention in the Middle Ages, by Frances and Joseph Gies
And while these are in no way scholarly, the easiest way to get a sense of who was living in a medieval forest and why, is to play Kingdom Come Delieverance (which illustrates virtually all of the groups I’ve listed), or to read Pillars of the Earth by Ken Follet (which for being historical fiction does a really good job at capturing the legal aspects of medieval life).

Besides u/SpeaksDwarren's excellent recommendation, life in swamps has also been discussed by u/epicyclorama and u/ThatHabsburgMapGuy, though more from a socio-cultural perspective, in this thread