Just finished reading your analysis of Bran III and I noticed you mentioned that the people of the Gift migrated South and swore fealty to Houses like the Umbers and the Mountain Clans. Was it legal to migrate and change your fealty in a feudal system? It seems to me this would be considered a betrayal.
The answer is that it depends a lot on what period we’re talking about. Under serfdom, it was not legal to leave the plot of land the serf had been assigned to and had tenure on, not least because they owed service in labor to the lord of the manor.
However...it is an absolute truism of legal history that if a law is passed banning something, there must be a significant number of people who had been doing the banned behavior. Serfs ran away from their land all the time, and while their feudal masters would try to hunt them down just like happened in the antebellum United States, whether they’d get caught had a lot to do with how much of a head start they got, how active the lord was in pursuing them, but most of all how far it was to the nearest town or city.
For medieval serfs, towns and cities were the great potential loophole in the feudal system, because unlike rural villages where everyone knows everyone else and strangers are really easily singled out, the anonymity of the crowd favored the runaway. With no system of identification other than the manor court rolls, it was really easy to change your name and loudly declare that you were a freeman and had always been so, and that you’ll sue if anyone claimed otherwise. (Incidentally, another thing peasants did all the time was sue their landlords to prove they weren’t serfs.) More importantly, a city with its own charter allowed the serf to claim burgher rights - usually, this involved being a resident for a bit more than a year and/or demonstrating that you owned property and/or by paying a fee - and once you had that right, you were now a free citizen of the city and no longer legally a serf.
Moreover, the nobility’s sense of upper class solidarity often didn’t fare well in the face of economic necessity: when lords needed to expand their labor force, whether because there had been a plague or a war that had left regions depopulated or because all that newly-cleared forest and fenland needed someone to work it, they often would offer various incentives to immigrants - which often included improved legal statuses as well as tax exemptions and cheap rents.
In that scenario, it behooved the lord to accept their new tenants’ word that they were totally free peasants and to get very aggro with any other lord who showed up trying to recover their runaway serfs, because how dare you challenge my right to offer free tenancy to anyone I want, and so on.