You hear of leaders (either deposed rulers or leaders of opposition/revolutionary parties) being exiled to other countries throughout history. If someone is exiled from the country of their wealth/familial land, how did they afford their lifestyle?
It depends on the situation.
Generally though, it would fall into one of two categories.
(a) The exile had the time and forethought to move some of their wealth abroad. For example, when Phillipino dictator Ferdinand Marcos fled the country in 1986, he is alleged to have squirreled away several billion dollars. Including several hundred million in cash, gold, etc carted away on the plane he fled in.
(b) They have friends/allies willing to sponsor them. Often this might be a deliberate decision by a foreign power to destablize their former country. For example, when Charles I was executed during the English Civil War, his son Charles II fled to France and was maintened by a grant from the King of France. France being traditional enemies of England. Until England and France allied together to fight Spain over the Spanish Netherlands, at which point Charles II turned to Spain for support in exchange for his Royalists fighting on behalf of Spain.