I was always under the impression it dependent on who owned their “contract”.
Good people let them go, the others didn’t.
The involuntary was “court” ordered, or ordered by the nobility in the UK.
I have read they even went so far and to order prostitutes to the colonies for “breeding” purposes.
My one ancestor came over under contract by his uncle who was trying to set up a nobility in the Conn River valley. Once he got off ship he hightailed it and somehow was made a freeman at Salem MA around 1636-38. How we do not know. Had to have been before 38 cause he filed law suit against a neighbor for livestock that knocked his fence down that year.
That is how I studied up on this stuff-genealogy is a time consuming thing.