Rather than quoting from serious academic articles, I'm going to use some simple educational websites. The History Learning Site states:
Who were slaves? They were people who were frequently captured in
battle and sent back to Rome to be sold. However, abandoned children
could also be brought up as slaves. The law also stated that fathers
could sell their older children if they were in need of money.
Similarly Spartacus Educational explains:
Slavery existed in Roman society from an early stage of its
development. There were several ways you could become a slave in Rome.
Some became slaves because they could not pay back the money they had
borrowed. The government would also take people into slavery if they
could not pay their taxes. There were also many cases of poor people
selling their children as slaves to richer neighbours.
So Roman citizens could technically become slaves (although it would be unlikely to happen at his age).
In the film, he had a home, but it was burned to the ground and his family left dead. At this point, his previous "life" is effectively done and he is now an unknown nobody. Except for the tattoo.
In the movie, the tattoo (SPQR: Senātus Populusque Rōmānus ("The Senate and People of Rome")) is on his upper arm. Vegetius (ancient Roman historian) confirms that soldiers were often branded, although he stated it could be on their hands to make it even more obvious if they had deserted. The punishment for desertion was Fustuarium (being clubbed to death). It does appear logical that, in the film, the slave owners who found and identified Maximus would have realised they could have lost a lot of money on a valuable slave if that had happened to him.
However, having said all that, it is worth remembering that it made for a fantastic story and so historical accuracy was not high up Ridley Scott's list of priorities. For more information on this, just check out this link which lists a large collection of the historical inaccuracies prevalent in the film.