A Canaanite slave (who's mother is Canaanite and father is foreign) is obligated in all negative Mitzvot which includes keeping Shabbos just like a Jewish woman (and some positive Mitzvot including Kiddush Bentching eating matza and Korban Pesach). He cannot become a slave to a Jew unless he fully accepts the Mitzvot and has to do Mila (circumsision) voluntarily and Tevila (immersion for the sake of servitude) Yevamos 48a
The Rabeinu Bacheye (13th Century kabbalist) in Exodos 21,26 explains that the Canaanite slave is a Tikkun (spiritual rectification) for the soul of the Canaanite forefather Cham who acted immorally with his father Noach and was cursed to be enslaved by others. This is the Kabalistic meaning why a Kenaanite slave goes free when his eye or tooth gets knocked out, since Cham sinned by seeing his father's nakedness, and by speaking using his teeth to his brothers about the act which he had done with his father, when the tooth or eye gets knocked out he has atoned for the sin of Cham and may go free.
וכי יכה איש את עין עבדו. מצות התורה בעבד כנעני שיצא בשן ועין, והטעם בזה מפני שלא נשתעבדו אלא בשן ועין, שנאמר (בראשית ט) וירא חם אבי כנען את ערות אביו ויגד לשני אחיו בחוץ, ראה בעיניו והגיד בפיו ונתקלל על זה ארור כנען עבד עבדים יהיה לאחיו וכיון שלקו האברים החוטאים נפטר הגוף מעונש עבדות.
So in answer to your question there is no forced subjugation as the slave has to accept Judaism otherwise cannot be a Slave. The reason why someone would do this is because of the spiritual need to Rectify his soul by accepting the Mitzvos (commandments)of G-d and realising that he can atone for his previous incarnation's sins and ultimately become a servant of G-d just like Eliezer Avraham's servant (a decendant of Cham) who was eventually freed and enterred Gan Eden alive (Derech Eretz zuta 1,5).