Before GPS updating was common, this was a common problem. En route, the FMS position would be derived from the INS which wcould and would wander. Your map oictire would wander accordingly. You would first be aware of it when the FMS took a more accurate fix off a navaid - usually the ILS when you intercepted on approach whne you could find yourself 'shifted' by up to three miles in a second. This 'map shift' could cause problems so the 'Map Integrity' check was there to warn you of it in advance.
Map shift is largely a thing of the past with GPS updating. The 747-400 I used to fly still had it in the checklist as it could still shift a little. The A320 I fly now doesn't and I have never seen a shift.