Can my landlord take half of my profit from a business sale?

[lifton]

So my parents own a restaurant that is currently on a month to month rent (i.e. no lease agreement because they decided not to renew it). They've been wanting to sell the business for quite some time. They finally found a buyer that's willing to buy the business and equipment and negotiate a new lease with the property management firm. Now they got a phone call from someone representing the firm saying they have rights to take half of the profit from the sale. Is this even possible? What regulation cites this right?