There have always been poor people and rich people.
Today however, the poorest american is wealthier than the wealthiest emperor of Rome of all time. And I'm not even joking.
Giving food to people was a common way to earn popularity and keep the peace. This was done because the Romans had a top notch agricultural system, best of it's time, and could produce a lot of food. Irrigation was top notch, etc. The fact that there is abundance is not sign of "collapse", it's a sign that things are going well and of progress and prosperity. Yes, politicians used that prosperity to garner votes and popularity but that's not to say that abundence in itself is wrong.
Jesus Christ man. The Church, after it became established, did a lot of charity in the Roman Empire.
Rome fell due to a lot of factors. Health was one -> as many said, lead poisoning was a serious thing. Romans were smart but it would be centuries after that people found the properties of lead, scientifically. The next thing was the separation between east and west. It was just the western roman empire that collapsed. The other was that there were too many enemies on too many frontiers. The next thing was tribalization of the army if you will. Powerful generals that lead large armies would earn the loyalty of those armies and then they'd make a civil war to become emperors. This was because the military stopped being made just by romans with roman values, but also of people who weren't fully romanized yet and they didn't have any loyalty to the notion of republic. They were loyal to the "strongman" in charge and to whom paid them.
So. Lead poisoning. [B]multiple enemies. Splitted empire. Fractured military. Barbarian invasions. Religious turmoil -> Christianity became the norm but not everyone in the empire wanted to be a Christian[/B]. Court intrigues.
The only way abundence played into this is because abundence made the Romans targets. That's it.