This is normal behavior. When you run a recovery plan in DR mode it will attempt to shutdown VMs at the protected site but if it is unable to will just continue with recovery plan.
What you are experiencing with the VM with disconnected storage is kind of a "zombie" VM. When you disconnect storage the VM often continues to run because there are a number of things stored in memory that allow it to function in a limited sense. As you experienced it may even be able to respond to pings. More than likely though it is really unable to do any work and therefore "dead" but not aware of it. Until vSphere 6 there was no simple way to deal with this. Now in vSphere 6 there is VMCP (VM Component Protection) which will monitor connectivity to VM storage and if an issue arises (like an APD or PDL) VMCP will shutdown the VM and restart it on a healthy host (eg. one that has access to storage).
Does this answer your questions?