Throughout the period there existed a class of landless peasants. These people survived through begging, banditry, and especially (very low) wage labor. If lucky, they might have been able to find a manor in need of a serf, but entering from such a position they would have been at the very bottom of the manorial hierarchy. They would have had a very hard time of it indeed.

To expand on Rittermeister's comment—so long as you were able to stay in your hometown, you could expect some community help. If you had any sort of living relations with financial means, you could generally expect to stay with them, as long as they were able to keep you fed. You would be expected to find piecework of whatever variety possible, or simply beg (although the legality of begging varied widely across Europe). If you live in a town of decent size, you could typically hope that the Church would provide food for you. If you were particularly lucky, a rich nobleman or merchant would have recently died, and stipulated in his will that a certain amount of beggars in the city would be fed for a certain amount of days. By the early modern period, civic poor relief began to appear in various places throughout Europe.

If you were exiled, if your hometown had no means to support you, or, worse, if your town had been sacked or struck by natural disaster (both not uncommon occurrences at various places and times): you were in huge trouble. "Foreign" homeless, meaning anyone not from the town or immediate surroundings, would typically be treated with distrust, hatred, and much less aid. Rolls of "native" indigents were kept, making it difficult for foreign poor to access poor relief, particularly from non-Church sources. Your chances of finding housing and work were even lower—with little else to do, most people of this description (typically men, since women almost always had something to sell) would wander fairly widely, begging whatever they could before being pushed or starved out.

There's a very old practice called "gleaning" which is akin to a type of welfare. Leftover crops would be collected to be distributed to the extreme poor. It's a practice that's been recorded in several cultures.

What class of people? Things were very different depending on your wealth and standing. Are we talking about nobles, wealthier and skilled peasants (proto-bourgeois, like millers, blacksmiths, merchants, etc.), or serfs/farmers?

Often a homeless man could find work as a hired labor.. most families during the time survived on almost subsistence culture. An extra hand meant more product in terms of agriculture but you would have to house and feed them in something resembling an adult family member. A woman of course who was homeless could be kept as a domestic servant. She could help run and clean the house.. take care of the children. If a woman was a seamstress she could help with that work as well. People could easily during this time become homeless if their family lost a plot of land for various reasons including death.