If one acquires a valid right by permit or lease to the oil and gas in any unsold public free school or asylum land under any other law, a subsequent purchaser of such land shall not acquire any rights to any of the oil and gas that may be therein, but when the rights under such permit or lease terminate in the manner provided in the law under which they were obtained, then the owner of the soil shall become the owner of that portion of the oil and gas herein relinquished, and shall be thereafter subject to the provisions of this law. A forfeiture of the purchase of any survey or tract for any cause shall operate as a forfeiture of the minerals therein to the state. A relinquishment to the state of a lease producing oil or gas in paying quantities shall not operate to relinquish or convey to the owner of the soil any interest whatever in the oil and gas that may be in the land included in said lease.