I am presuming this would be someone living in Rome at its height (e.g., 2/3rd century AD) who got the full ration of bread, olive oil, etc.
The Roman grain dole was not really a "poor relief"--this paper does a really good job covering the basics. Furthermore, I don't believe that the dole would be able to cover the full subsistence of a family. So, that said, they would probably be working. The idea of a slave based urban economy has rapidly fallen out of fashion, and I strongly suspect that the desperately poor of ancient Rome would be doing the same sorts of menial, temporary labor done by desperately poor throughout urban history.
http://www.reddit.com/r/AskHistorians/comments/1ck02l/did_ancient_societies_have_problems_with/
This thread has some relevant answers around land reforms and the shadow economy.