What I do to solve this issue is each group has a cubby where their unfinished work goes. This is great for on-going assignments as well as unfinished work. At the end of the day, whatever work is not completed (and is not an on-going assignment), I pull out of their cubby and put with the outgoing homework. Essentially, any work unfinished goes home as homework and must be returned the next day. This is also a way of differentiating for the students who work more slowly, as they are given additional time without penalty.
What about the rest of you? How do you manage unfinished work?