Yes, it was common for enslaved people in Rome to ‘earn’ a little money. This was often in the form of tips but, as Gaius, a Roman jurist, wrote in the second century AD, “whatever property is acquired by a slave is acquired by his master” – whether the slave kept his or her ‘earnings’ seems to have been at the master’s discretion.
If enslaved people saved that money, they could use it to buy their freedom for a sum agreed by their master. The Romans had an official system for freeing slaves that was unique in the ancient world.
Called ‘manumission’, from manumissio, (‘release from the hand’ of power), it came in several forms: the most formal involved a magistrate, and gave the freed slave not only his freedom, but also the right to trade and make his own living, as well as to make and to benefit from a will.
Lifelong obedience and services (obsequium et operae) towards the former owner were part of the deal, and a freedman (libertus) remained part of the familia, the ex-owner’s extended household. Less formal forms of manumissio even meant that when the freed slave died, everything he had reverted to his former owner.
Answered by Gillian Hovell, author of Roman Britain (Crimson Publishing, 2012)