[EKS] [request]: EBS volume provisioner for StatefulSets

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**Tell us about your request**
Currently when using EBS for PVs the Stateful Set (or at least each of its pods) is bound to only one availability zone. Would it be possible to "migrate" the EBS volumes across availability zones in case a new pod is scheduled in a different az?

**Which service(s) is this request for?**
EKS (PVC, PV, StorageClass)

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
My application requires a persistent local filesystem. Right now I'm using Stateful Sets to achieve that, kubernetes wise it works well. However in case in which the node my pod runs on gets terminated it stops working as expected. Let's go through an example:

* ec2 instance 'i-abcd' runs in availability zone 'a' and belongs to an auto scaling group 'asg-foo'
* i-abcd is the only node in the cluster
* asg-foo's launch configuration is set to spin up instances in all the available availability zones that are available
* pet-0 pod (part of the stateful set 'pet') runs on instance i-abcd
* pet-0 has a PV associated which is an EBS volume 'vol-1234' which is located in availability zone 'a'
* i-abcd gets terminated
* asg-foo spins up a new instance 'i-wxyz' in availability zone 'b'
* vol-1234 cannot be attached to i-wxyz due to availability zone mismatch
* pet-0 is forever in pending state

**Are you currently working around this issue?**
EFS storage class is AWS' recommendation, however NFS in this case is being used for single machine just to work around the az limitation. So in this case EFS' multi az capability is being used. To paraphrase Larry Wall's words: It's like trying to club someone to death with a loaded Uzi.

Start by researching the EKS PVC, PV, and StorageClass behavior described in the issue, along with StatefulSet scheduling across availability zones. Verify the EBS attachment limitation and define what supported volume migration would require; done would mean a clear implementation path or documented resolution for pods rescheduled into another zone.

Written by the indexing model from the issue text.