A lien under AS 34.35.320 - 34.35.390 binds all the right, title, and interest of the person at whose instance or request or for whom the work is performed or material furnished, to the full extent of the interest that the person has at the commencement of the work or at the time the material is furnished, for which the lien is claimed, or subsequently acquired up to the time of foreclosure of the lien, in (1) all of the product or output of the cannery, saltery, or other plant or establishment for which the material or work was furnished; and (2) the plant or establishment itself, including the houses, wharves, machinery, and equipment.