There were certainly people who existed outside of the feudal system, such as thieves, beggars, and various wanderers and itinerants. I can't supply many specifics about them, hopefully someone else can. But as for support for the 'unemployed', the Black Death was really the turning point for charity and welfare, at least in England (which is the area I'm most familiar with).

Before the plagues charity often came from family members, but after the plague wiped out families and communities, wealthy people set up hospitals and almshouses where the poor could receive help. It was through church parishes that they would gather money to provide for these people. However the people who lived in these almshouses were carefully selected, omitting drunks or the 'feckless', however that may be interpreted.

So from this you can see that certain people were seen as freeloaders, and these people were often barred from receiving help. Eventually, in the 1600's, many beggars and thieves would be shipped off to North American colonies against their will. So they were very much seen as a burden, at least in England. I can't really speak for other feudal societies.

I know guilds also provided kind of an 'insurance policy' to members, and they would gather money for the families when a guild member passed away, and they provided for those guild members who were unable to work.

Sorry, not the most comprehensive answer, just a broad idea; hopefully someone else can provide a more detailed explanation.

Sources:

Christopher Dyer, The Economy and Society, from The Oxford Illustrated history of Medieval England.

Allen Taylor, Colonial America. (for the bit about beggars being sent off to the new world)