That's the failure mode for bad disk, but are you saying that in the normal case of live migrate (eg BIOS update needs to be applied to host machine), that the (data on the) local SSD is a also seamlessly moved to the new host, seamlessly and invisible to the guest VM?
Yes, under a graceful live migration with no hardware failure, the data is seamlessly moved to a new machine. The problem of moving local data is ultimately no different that live migrating the actual RAM in the machine. The performance does degrade briefly during the migration, but typically this is a very short time window.
