How does an FMS shift after losing all external navaids? It's not uncommon for polar flights to lose GPS signal (ionosphere issues due to the high latitudes). But it is not a concern because the typical IRS drift is 650 meters for every hour of flight, and the skies are empty (compared to the Atlantic tracks) in those regions.

Sooner or later GPS will be back, navaids will be within reach, and radar coverage will resume.

Q: Now, what happens when the GPS signal is lost? Does the FMS navigation start to drift from this point on, or does it switch to all the accumulated IRS drifting that's been going on for hours prior?

One way to picture the latter (I guess), is the magenta line on the navigation display to abruptly shift away from the plane-symbol, even if it is just by a mere few nautical miles.

My question applies to the older IRS systems that require stationary alignment, unlike the new GPS-coupled align-in-motion systems found on the 787, etc.
Turns out indeed it's an issue affecting polar operations. It differs from type to type, but for the 737-600/-700/-800/-900 as an example, the message UNABLE REQD NAV PERF-RNP will be displayed.

For oceanic areas this will only happen if ANP shifts by over 10 NM, i.e., after losing the RNP-10 capability.

At an IRS drift rate of 650 metres per hour, it would take 28 hours of being airborne or a rather shifty IRS unit—no pun intended—for the message to be displayed.

So the answer is that the magenta line won't shift, unless the pilots choose an IRU over the rest by using the position shift function of the FMS.

For the 747-400:


  When no global positioning system (GPS) updating occurs, all position and velocity corrections gradually are phased out until the FMC navigation parameters equal the selected IRU position and velocity.


This logic is part of the RNP standards and regulations, to stop an auto flight system from chasing the course when navigational accuracy becomes questionable. Any loss of GPS (away from ground navaids) inhibits the FMS from applying any corrections without crew intervention.



Source: Polar Route Navigation