A New Era for the Smith House

While it's obviously being exaggerated for comic effect in the episode, in real life squatters rights don't apply for a very long time, years in fact, not a month like with Dick. The basic principle behind squatters rights is if someone lives in a house, or occupies property, for a continuous period of time (without the legal owner being present) they can eventually become the legal owner, especially if they have been paying the property taxes; the main reason for the law is to prevent property from being in perpetual limbo (legally speaking) if the legal owner dies without any heirs to inherit said property or abandons it, otherwise it could never be owned again. The national average for squatters rights to apply is 10 years of continuous, exclusive and open occupation. In some states like New Jersey and Louisiana it takes 30 years for squatters rights to apply, Montana and California have the shortest window of only five years; and in some states squatters rights apply sooner if the occupants have been paying the property tax but the legal owner hasn't.

References Avatar: The Last Airbender (2005)