This is a big simplification but it has a grain of truth to it (so to speak). From the time of Gaius Gracchus, certain Roman citizens were entitled to the corn dole (frumentatio), a state-subsidised distribution of grain. This was brought about by the growth of the Roman population to a point where local farms could no longer supply her citizens.

The migration of Italian farmers to Rome probably caused the introduction of the frumentatio much more than the frumentatio caused the migration. For some time before, small family landholdings had been consolidated into latifundia, large farms owned by wealthy Romans. After successive wars, a glut of slave labour from prisoners of war made this consolidation much more economical. Consequently, displaced farming families, or free agricultural laborers, moved to Rome. This only aggravated the need for a grain dole.

The frumentatio survived Gaius Gracchus for centuries. While successive magistrates and emperors continually changed the rules of eligibility for the dole, it was a fixture of Rome's economy well into the imperial period.

Also keep in mind that this grain dole was not aimed solely at the poor. This being Rome, plenty of wealthier people with connections would find themselves on that list. Lastly this wasn't welfare from our modern perspective, but more to ensure the stability of the state - to prevent grain riots from breaking out.

Any book recommendations for Roman farming and Roman economic life between the end of the Punic Wars and Augustus? (Or better yet, all the way to 476AD?) I ask because I often wonder about this 'drift to the cities' how much of it was caused by the 'pull' of city life and how much much the 'push' as smaller farms lost economic viability. Or even the possibility that we misunderstand the phenomenon altogether.

Weren't Roman citizens given land at the end of their military service. It seems odd to pass up on the off chance that things might be politically unstable enough to pass out free food.