In this doomsday scenario, the network would probably stop working properly a few blocks afterwards, until a coordinated hard fork.

We know that the block's timestamp has to be less than the median time of the last 11 blocks plus 2 hours. If the 99% of the hash rate disappeared, the difficulty would drop by 25%, but this wouldn't be enough to retain the 10 minutes rule, but neither the process of the BIP113 soft fork overtime. Initially, the miners would be more vulnerable to have their blocks rejected, unless they altered the timestamp to an arbitrary valid value.