Shared Nothing Live Migration protects you from planned downtime (say you need to patch Windows on host or replace or upgrade some hardware components). See:

Shared Nothing Live Migration

For an unplanned downtime you need either VM HA (little downtime, little data loss, VM reboots) or guest VM cluster (no downtime, no data loss, VM turns to other host). See:

VMs for High Availability

Guest VM Cluster for HA

Both require some sort (physical or virtual) shared storage. For physical you may need CSV configured on either Clustered Storage Spaces or iSCSI or FC SAN or SMB3 share. See:

Storage Type Description
Shared virtual hard disk New in Windows Server 2012 R2, you can configure multiple virtual machines to connect to and use a single virtual hard disk (.vhdx) file. Each virtual machine can access the virtual hard disk just like servers would connect to the same LUN in a storage area network (SAN). For more information, see Deploy a Guest Cluster Using a Shared Virtual Hard Disk.
Virtual Fibre Channel Introduced in Windows Server 2012, virtual Fibre Channel enables you to connect virtual machines to LUNs on a Fibre Channel SAN. For more information, see Hyper-V Virtual Fibre Channel Overview.
iSCSI The iSCSI initiator inside a virtual machine enables you to connect over the network to an iSCSI target. For more information, seeiSCSI Target Block Storage Overview and the blog post Introduction of iSCSI Target in Windows Server 2012.

For virtual you may use either VM-running (slow and raises “egg and chicken” problem) or native virtual SAN.


Virtual SAN (no hardware storage)

You’ll have a configuration similar to this picture (below). See:

So no physical shared storage, SAN emulated from DAS. High performance (no network I/O) and fault tolerant (even with a pair of nodes all components are at least duplicated).