You don't DELETE a non-existant person.
You DETACH a non-existant spouse.
In People Workspace
Select the person with the phantom spouse.
Menu > Person > Attach/Detach > Detach
The next screen will list all relationships that person is in as a spouse, child, and parent.
One should be the Phantom Spouse.
Select the radio button next to that relationship
If that doesn't work, I can only guess that you have somehow created these from some kind of import and is probably not fixable without going back to the original file and correcting the situation in the original file and re-importing the correct info.