Not that I think this system would work, but people do volunteer without being paid: charity, soup kitchens, etc.
There aren't many volunteer organizations that, to borrow dgallagher's example, mow lawns or rake leaves, and the ones that do, only do it for special places. Perhaps for a monument or a park.
The attractive part of basic income for me is that everyone has enough to buy food and housing, so suddenly menial laborers have an iota of bargaining power.