Did they continue to be government officials? Were they suddenly private citizens? Were their properties confiscated?
In the immediate aftermath of Odoacer's declaration of the Kingdom of Italy, and the consequent deposition of Romulus Augustulus (and prior reduction of Julius Nepos to absentee figurehead), the Roman senate continued to exist, and continued to be what it had been for several centuries by this point: a body with no real authority, but some consultative role, this time for the Kings of Italy rather than the Emperors of Rome. This continued for some time under the Odoacer's kingdom, under the Ostrogoths after Theodoric invaded Italy and overthrew Odoacer, and under restored Roman rule after Justinian's Western campaigns.
No one knows exactly when the Roman senate disappeared. It still existed in 603, but probably not by 630.