After sale made as provided in the preceding section [48-3-14 N.M. Stat. Ann.], the proceeds of such sale shall be applied to the payment of the costs of advertising and making the sale and the satisfaction of the demand of the lien claimant, and the residue, if any, shall be refunded to the lien debtor; provided, that the lien claimant shall not be precluded from bidding on or purchasing the property at such sale.