Tom and/or Ghav could cover the subject better, and will likely correct my own errors, but neither dependency nor voting themselves welfare killed the Athenians democracy. "Depending" on how one defines it, "the fall of Athenian democracy," it was either due to losing the Peloponnesian War prompted by the rest of Greeces resentment to growing Athenian hegemony, or Philip of Macedon exploiting and prolonging the resulting Greek divisions to install his own hegemony.

Rome would, superficially, be a better parallel (it usually is when referencing the US republic, either openly or via specious quotes from Nineteenth Century British political scientists,) but even there the specifics do not fit. Roman dictatorship resumed due to conflict between patricians and the growing, increasingly restive, underclass including current/former slaves, newly allied (through conquest) local tribes and landless citizens. Sulla revived Romes dictatorship to lead patricians AGAINST that underclass in the Social War, which naturally resulted from conservative assassination of the reformer Gracchi brothers (who often remind of JFK and RFK.) In the process he imposed a bloody purge of reformers, taking their lives and property as well as barring their surviving family from political office. Julius Caesar was among those familes, but spared thanks to influential friends in common with Sulla, despite (according to Seutonius) Sullas presciention Caesars ambition and reformer sympathies would make the Republic rue his mercy.

After winning the Social War Sulla dutifully resigned his dictatorship, restored the Roman constitution and retired to his estate to write his memoirs. Yet his was the precedent Caesar and all subsequent Roman autocrats invoked to justify their own military coups and expansive unconstitutional powers. Sulla proved an influential conservative with a sufficient army could set aside the republic, and that only his voluntary submission would allow its resurrection in that event. It certainly was not a case of citizens crippling their democracy (or republic) by voting themselves welfare; that was the sort of thing Romes patricians assassinated two consuls, abrogated the constitution and fought the Social War to PREVENT.

All for naught; so long as the systems inequities remained the resulting need for populists to address them (and thus opportunity for demagogues to exploit them) remained with them. Sulla could and did exterminate one generation of reformers, but even had he not spared Caesar a Pompey or Anthony or Augustus would have come along sooner or later to ride popular discontent with the wealthy ruling class to power. Ignoring problems and/or killing the messenger does not banish them, which is the real lesson to take from the Gracchis deaths and the supposed patrician "victory" in the Social War that was the beginning of the end for the Republic.