The unclean spirits in the NT are also known as "demons". This is confirmed by BDAG in the entry for "diamon", see below.
Let us begin with the venerable BDAG which has two entries about "demons" which I will list below.
"diamon/diamonos" is an (evil) spirit/demon … Matt 8:31, Mark 5:12, Luke 8:29, Rev 16:14, 18:2.
"diamonion" is either a (1) transcendent incorporeal being with status between humans and deities, daemon, semi-divine being, a divinity; spirit, (higher) power. eg Acts 17:18; or, (2) a hostile transcendent being with status between humans and deities, spirit, power, hostile divinity, evil spirit, eg, Luke 8:30, Matt 11:18, Luke 7:33, 8:27, John 7:20, 8:48f, 52, 10:20, Luke 4:33, 35, 42, ...
Nowhere does the Bible or NT specifically, describe these demons as souls of people. However, it does describe these demons as occasionally inhabiting humans in the sense of taking over their minds. Mark 5:15 and Luke 8:35 both describe a man that had been purged of demons that was then "in his right mind".
We are also told that such demons/unclean spirits are subject to the disciples (ie being able to exorcize them, Luke 10:17) and to Jesus (see above list of references).
There more fascinating data available that is tantalising in its brevity. Some demons recognised Jesus as who He was - the Son of God (Matt 8:29, Mark 5:7, 8, Luke 8:28, 29, etc). Further, James 2:19 states that the demons believe that God is one, and shudder!
Lastly, these demons appear to know that some (presumably future) time Jesus will imprison them for "torture" (Matt 8:29, Mark 7, 8, Luke 8:28, 29). This place is called "abyss" in Luke 8:31 but is otherwise unidentified. The book of revelation makes much use of this "abyss" in places such as Rev 9:2, 11, 11:7 17:8 (all describe the abyss as the origin of the beast and associated beings), Rev 20:1, 3 (beast is thrown back into the abyss). Rom 10:7 also describes the abyss as the place of the dead suggesting the dead and demons occupy the same mythical place.
There are numerous theories about exactly what demons are and where they come from and their function but I will not discuss these here as all are theologically based and not hermitically based.