Depending on the model, variant of the FMS, different things can happen. On the MCDU PROG page, you can see the predictive GPS req'd, estimated, and accur values. Looking at this page can give an explanation of the "PRIMARY LOST" or "GPS UNAVAIL".
The different boxes have different features with a hybridized HIL that estimates when GPS integrity falls below certain limits, creating an 'equivalent' HIL, but for short amounts of time, which differs depending on equipment. Usually the time of the hybrid HIL is linked to the IRU, but most are in the 6 to 7 minute range where the FMS will estimate the time to reach HAL, and therefore the error messages.