Abstract: The invention relates to a safety device that ensures longitudinal sealing of the shaft of a primary pump following the rupture of one of the seals separating the high-pressure chamber from the low-pressure chamber of the fluid in the pump, the device made up of a hollow piston comprising an upstream side part of outer diameter D1, and a downstream side part of outer diameter D3, greater than D1, the piston coaxially surrounding the shaft and being placed in a chamber made in the seal housing, the device also comprising activation means which axially move the piston against the shaft when a seal ruptures, wherein two annular chambers are made on the downstream side of the piston, the first, whose outer diameter D2 is greater than D1, communicating with the low-pressure chamber.