In my environment we are using host named site collections for a service that we offer to our clients. Each client has their own site collection and for security and data isolation we use dedicated content databases for both the SP and the Nintex databases. Occasionally a workflow or two will start acting wonky (usually after we upgrade our 3rd party software that we use Nintex to interact with). With over 160 clients you can imagine that it can be more than a couple having trouble and while we do get notified when workflows fail, sometimes a failing workflow is elusive. That's where PowerShell comes in. It may be possible to do this via CSOM but I've not experimented with that much. Using CSOM would let you write a script on your desktop and run it against your farm. It really depends on your permissions.

The trick to finding these workflows is looking at the workflows that are running on an item. Workflows in our environment run against SPItems though we also have a few that run on SPSites. 

After getting a reference to the spWeb and spList of your choice it's just a matter of looping through each item and inspecting each workflow, looking for the info you're after. The ParentAssociation.Name is the name of the workflow that you're looking at. In the example below I am looking for all previous versions on an item and writing them to a log if their state is Running, Faulting, Terminated. You can find your workflow names on the List under "Workflow Settings." in the ribbon. You can find internal states here.

foreach ($item in $list.Items) {
  foreach ($wf in $item.Workflows) {
    if($wf.ParentAssociation.Name -like "*Previous Version*"){
     if($wf.InternalState -match 'Running, Faulting, Terminated'){
     $counter++;

     write-output $item.ID "|" $wf.InternalState "|" $wf.ParentAssociation.Name  | Out-File $outfile -Append}
}
}
}

I have attached 2 versions of the script. One is for looking up workflows on a single list in a single site.Since I have vanity URLs I pass the sub domain and the name of the list for it to query. The second one is the farm one that looks at every workflow on every item on every list on every site on every web application in your SharePoint farm. It sounds like it would peg your CPU and chew up your RAM but its not bad. Try it on your DEV or QA farm first. 

I hope you find these useful and if you have any recommendations on improving them I'd love to hear them.