After looking at the files that "editoremma" sent and trying out some things, here's what fixed the problem.
As a preliminary check, here's one thing that pointed the way to the solution.
Double-click on the resourcepool to open it. During the open process, there will be a popup "Open Resource Pool" with 3 options. Choose the 3rd option "Open resource pool read-write and all other sharer files into a new master project" and click on OK.
You may see a warning (exclamation mark) message "The file for resource pool consolidation cannot be opened" and a specific file will be shown in the message. Note the filenme and click on OK to acknowledge the warning. Even though only one file is named, there can be multiple files causing the problem.
On the menu bar click on Tools > Resource sharing > Share resources. This display shows all the files which have been linked to this resource pool.
By manually comparing that list with the files, it was possible to identify 3 files with issues: two were no longer available and one had the phantom assignments. You can see which had the phantom assignments by checking out the pages editoremma provided links to.
The fix?
To eliminate the phantom assignments in one file, I had her create an empty project file with the same name as the file that had the phantom assignments and placed it in the folder where Project was expecting to find it. (Again, look at her links to see the filenames in the Project Name column.)
Then she exited from Project; double-clicked on the Resource pool; in the popup dialog "Open Resource Pool" she selected the third option "Open resource pool read-write and all other sharer files into a new master project file. You can access this new master project file from the Window menu command" and opened the files.
In the menu bar she selected the window with the Resource Pool and then clicked on File > Save and exited from Project.
That fixed her problem.
If you are using a resource pool and a master project then periodically you should consider opening the resource pool, clicking on Window > xxx (where xxx is the resource pool window), and then clicking on Tools > Resource sharing > Share resources. In the popup, manually confirm that you are still linking to the files you expect to be linking to.