People could and did sell themselves into slavery, but I am unaware of any limited terms of slavery. Maybe they existed; I don't know. I do know that a "δούλους" was most definitely a slave, but generally this was not a bad status. A "δούλους" could earn money and have property that was his and not his master's for example.
What we generally think of as a slave was called a "σκλαβος". These people were generally captives of some sort and were not at all treated well. For example, they were worked to death in quarries and the like.
Being a "δούλους", as I said, was not a bad thing in the context of the times. Many "δούλουoi" had a higher societal status than poor freemen and many more certainly were better educated.
When a Greek Orthodox priest gives an Orthodox Christian communion he says:
"Μεταλαμβάνει ὁ δοῦλος τοῦ Θεοῦ (Name) σώμα καὶ αἵμα Χριστοῦ, εἰς ἄφεσιν ἁμαρτιῶν καὶ εἰς ζωὴν αἰώνιον. Ἀμήν."
"The servant of God (Name) receives the Body and Blood of Christ for forgiveness of sins and eternal life."
I think we all have to be on guard against allowing our Western, Enlightenment mindset distorting what The Faith is saying to us. To be called "ὁ δοῦλος τοῦ Θεοῦ" is, or at least should be, the greatest joy for us.