Why did the believing Jews stay in Jerusalem instead of going back home to Rome or Babylon?
They believed Jesus was the Messiah and that the King and Kingdom were just over the horizon, so they saw no reason to return to Babylon, Rome, Spain, or North Africa among pagan Gentiles. Instead they stayed in Jerusalem and lived from the common fund as a stopgap until the King would come.
Les explains that after Pentecost, Peter and the eleven preached, and many Jews believed Jesus was the Messiah and that the Kingdom was coming. Since Israel’s belief would bring the King, these believing Jews expected the King and Kingdom just over the horizon. They reasoned, why go clear back to Babylon, Rome, Spain, or North Africa to eke out a living among pagan Gentiles when the King is coming? So they stayed in Jerusalem and lived out of the common kitty as a stopgap until the King would come and the Kingdom would be set up. But Israel did not respond, the King did not come, and the kitty ran out. They ended up poor, having sold their goods, and were caught in Jerusalem, perhaps unable to buy a ticket home. Les teaches that God is just and would care for them because they had believed the Gospel of the Kingdom. This care came through Paul’s agreement with Peter, James, and John to remember the poor saints in Jerusalem.