They simply would cease to exist. There are no state paid employees or huge tracks of land that are owned by the Federal government. Each trail system that goes through an area is there because a private landowner has graciously given his consent to let the trails exist there. Someone has to talk to the landowner and assure him that the trails will only be in a certain area of his land.
Someone has to plan, brush, put up the signs and groom the trails.
This is done through clubs on a volunteer basis. Money for equipment, upkeep, signs and organizational fees come from club members dues, gracious donations by local businesses, support from the AWSC and club sponsored events such as grass drags, raffles and water crosses.