There were people who left the elites in Rome when they wanted social changes. What was that in early Rome?

You’re thinking of the Secession of the Plebs (secessio plebis).

In early Republican Rome, the lower class citizens — the plebeians — literally walked out of the city in protest against the patrician elites. This wasn’t symbolic. They physically withdrew from Rome and camped outside the city, refusing military service and civic participation.