The first act of Haydée's life is sad – she sees her own father get gunned down right before her eyes and is sold into slavery – but it's the second act that's more worthy of analysis. You'd expect the Count of Monte Cristo to make that all go away, and he does – sort of. He puts Haydée up in posh digs, gives her servants, and generally lets her do what she wants, as long as she doesn't leave the house. Also, she's his slave.
This kind of treatment certainly seems depraved today, and it doesn't really jibe with the Count's image as a righteous avenger. Determined to execute his plan, Monte Cristo goes to great lengths in order to make sure each cog in the revenge machine stays in place (read up on Bertuccio to see more on that). Haydée is no exception to the rule: she's a key element in his plan to "get" Fernand, but the whole slavery thing seems a little unnecessary. "God forgive me," Haydée tells the commissioner of the panel set up to judge Fernand, "though I am a Christian, I have always thought to avenge my illustrious father" (86.120).
So, if Haydée has enough riding on the betrayer's conviction to keep her sticking around, why the slave shtick? Well, you can say that about a lot of things the Count does. Why "Sinbad the Sailor?" Why "Lord Wilmore"? A lot of Monte Cristo's plans require the maintenance of an illusion, and few things scream "ultra-powerful, mysterious figure" than keeping a beautiful Greek slave-woman in tow. Also – and this is a bit creepy – his final declaration of love to Haydée becomes that much stronger as a result. He frees her literally, he frees himself of the whole "mysterious nabob" persona, and he finally lets go of his infatuation with Mercédès once and for all. It's a dramatic way to demonstrate a dramatic change of heart.