If you power off the node by unexpected power off (not graceful shutdown), cluster can't live migrate the VM. As you have described, it will be booted on the available node. Live migration is not possible, because compute resources of the VM (CPU, RAM) went offline, thus, they cannot be migrated. Failover cluster ensures high availability of the cluster roles.
If you want your VM/resource to be always online, you would it to be Fault Tolerant. Might be helpful:
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