Horse stopping method and apparatus

A method of mitigating the risk of a horse fleeing and becoming lost, comprising:

• fastening a horse-stopping apparatus for slowing and stopping a horse after a rider has been involuntarily separated, the horse wearing a head piece and a saddle, wherein the horse-stopping apparatus for slowing and stopping a horse after the rider has been involuntarily separated comprises:
• a leading segment configured to be detachably fastened to the horse's head piece;
• a trample segment fastened to the leading segment;
• and,
• a trailing segment detachably connected to the trample segment by a connector, and the trailing segment also configured to be detachably connected to the rider, the connector having a lower yield strength than the trample segment or the trailing segment;
• whereby if the rider is involuntarily separated from the horse, the trailing segment will extend the trample segment and the forward motion of the horse will carry the trample segment under the hooves of the horse;
• whereby the hooves of the horse will trample the trample segment thereby pulling the horse's head downwardly and thereby slowing and stopping the horse.