Could it change? Yes. Was it likely? No. The easiest way social class could change was to be a woman and marry someone of a higher class. This was still rare as noble families required doweries to keep their wealth. Marrying a poor woman would not really accomplish that. Marriage for love was not as common back then as it is today. For men it was more difficult. Joining the Catholic Church as a priest one could rise the ranks if you were smart enough to play Church politics and reach a status of cardinal. Also warfare and plunder could allow one to amass wealth and marry into wealthier families if you had enough gold and people feared you enough. If you were a peasant farmer you were more likely to die a peasant farmer as would your children grandchildren etc. The Middle Ages was not a capitalistic system. There was no buying your way or earning your way to the top. Social hierarchy was much stricter and solid in those days. So In the end, Was it possible to move up a class? Yes. Was it probable? No.
