I often wondered about the term, "settled minister" -- since I come from a long line of wanderers.
It seems it dates back to two elements of English Common Law, which our Puritan forebears brought with them to New England.
Towns and parishes were responsible for the poor "settled" among themselves, but not for wanderers and vagrants.
To have a gift of property "settled" upon oneself, as daughters of the propertied classes often were with a dowry in marriage, was a second Common Law practice.
Thus, when a New England parish called a minister to "settle" among them, they were saying that they undertook responsibility should he become disabled, as at least one of their own poor.
Some parishes, also seemed to realize that they were undertaking a life-long commitment on the order of marriage. In order to attract a minister, offered a "settlement" as an incentive: property on which to build a house of one's own; use of an existing parsonage; the right to tether a cow in the town common, or to so many cords of firewood from the town forest, etc.
We used to have a "Settlement Office" at the UUA. Now we have a "Transitions Office." Probably more honest. That's where I found my cow tethered.