Re: the desirability of owning a possessed slave, that’s historical. Because normally, one would think that one would wish to rid oneself of a slave that was sick or damaged in any way… but that doesn’t seem to have been the case all the time. (Old slaves usually got sent to the country, to a farm, to die doing harder manual labor than what they used to do in the house or manufactory; or they just got offloaded somewhere. It took a kind owner to free an old slave or pension him off to easy labor.)
There was always somewhere worse to send a troublesome slave, especially if there was a teensy bit of money to make off it.
Re: the reasons why a slave might become possessed, that’s informed speculation.
Humans are the heirs of Adam, made in God’s image. No human, even an unbaptized pagan human, can be possessed by a demon without some kind of consent or opening through sin.
This slave girl was not possessed just because her masters were doing something wrong; at some point, she was doing something wrong herself.
Cursing was a very big business and hobby in the Roman world. You could do it yourself, or you could go to a professional in the neighborhood. Archaeologists are always finding Roman curses on potsherds thrown into wells, and that sort of thing. (If you could write, or if your neighbor could write, it seems to have been regarded as making curses more efficacious.) If you had any kind of grievance against anyone, and you were powerless to do something about it, you would curse him, in the hopes that the gods or demons or magical forces would avenge you.
Re: assuming that a slave was born into slavery – That’s a pretty safe assumption in the 1st century, unless a slave has a Persian or German name. A lot of the Roman Empire’s economic and civil troubles were because they already had tons and tons of slaves from their previous rounds of empire-building, almost all of whom had slave children. Any trafficking in enslaving people was going to either be exotic people (from outside the Empire), or debt-slaves (not super-common in the 1st century, although it became a Really Big Thing as time went on and the Imperial taxes rose).
Now, it is possible that this particular slave girl’s occult possession was exotic enough. But it wasn’t, really; it’s very Greek to be possessed by a “god” and say oracular things. I mean, heck, that’s the Oracle of Delphi right there.
Now, if this “talent” was troublesome to her parents, and her parents were poor, that could lead to being sold into slavery. But again, that would have been a little unusual in the 1st century, because times were pretty good.
Yes, there are a lot of scenarios. But some are more likely than others.