Most people have, at one time or another. The most simple example is when you get blue-lighted and pulled over, and you jolly the Cop out of writing you a ticket.
A dispute arises where the ownership of a piece of land or a tree, or a boundary is the subject. The parties get together and agree without going to court, or a third party acts as mediator, and an agreement is found.
A divorce is contemplated, and a marriage counsellor or a priest/preacher meets with the parties and make them kiss and make up.
A Contract is disputed as to terms or whether specific performance has been completed, or the amount of money owed is in dispute. The parties Lawyers get together and work out a solution that is accepted by the parties.
I have been involved in all of the above at one time or another. Lawsuits were never filed, nor any public record made.
I venture to say that most of all disputes are settled out of court, w/o any suits filed or cases made. Litigation is expensive, and the main job of most lawyers are to stay out of courtrooms whan they can.