Molding unit (1) for the forming of a container (2) provided with a hollow recess (3), comprising: a mold (5) provided with a lateral wall (6) defining a cavity (7) and provided with a pocket (9) that comes out into the cavity (7); a boxing device (11) comprising: an insert (12) mounted in translation in the pocket (9) relative to the lateral wall (6) and provided with at least one passage (81) opening out; an actuator (16) integral with the insert (12) and provided with a piston (17) mounted in a chamber (22) defined in the wall (6) of the mold (5), the piston (17) subdividing the chamber (22) into a rear half-chamber (22A) in communication with a primary fluid duct (46), and a front half-chamber (22B) in communication, on the one hand, with a secondary fluid duct (50) and, on the other hand, with the pocket (9).