Legally speaking, slaves could not earn or own property of any kind. Legally all a slave's possessions were the possessions of his master. However, Roman law allowed for the peculium, the administration of assets legally owned by the master. Originally the peculium was intended for use by a father's sons, who legally had no property rights until the death of the pater familias or their emancipation by him (a comparative rarity). However, the peculium also applied to slaves as well. The possessor of a peculium was granted administrative access to certain assets defined by the master, and then was able to treat it as if it were legally his own property--in other words, possession of a peculium granted one the legal fiction of private property. The peculium could include not just money, but businesses, land, and even other slaves--there's a passage in Petronius where the main characters come into possession of a slave boy who is essentially gifted to them by the slave who "owns" him. The assets included in a peculium also could be handled by the slave or son totally independently of the master's approval or even knowledge--in all but legal fact the peculium was private property. The statuliber generally gained his freedom by returning his peculium to his master's administration, including whatever profit he had made on it. Therefore "purchase" of one's freedom consisted essentially of increase of a particular portion of the master's property, usually of a previously-defined amount.