Cannot remove a broken view (view ID and Name are $null)

A particular user is having issues with a specific list, and this seems to cause further issues with the list in general.

After some digging around it would seem there's a strange view on this list; the view in question has no ID, no Name, no Query and barely any data. 

We've tried setting the ID of the view manually (property is read-only). We've attempted to set various properties of this view, like the Query or Name only to receive an "Object reference is not set to an instance of an object" error. Obviously we can't delete the view itself, as the $list.Views.Delete() method requires an actual GUID as the parameter, and won't accept $null.

Any idea what could be wrong and how to delete this view?