The unit (1) includes a packaging (2), an applicator (3), and a product P to be applied. The applicator (3) includes an application element (12) that is housed with the product P in a reservoir (8), an internal handling part (13) that is placed in a holding housing (11) which substantial relative rotation cannot occur. A part in the shape of a rod (14) is housed in a pipe (10) that the rod is rigid enough not to break when the packaging (2) is folded crosswise for the purpose of opening break. The unit (1) also includes two holding zones for the purpose of the break fold in a fragile transverse zone (16) with lower strength.