Assuming you are talking about MS Publisher, Right click on the file to bring up the context menu.

Select: Open With
If Publisher is not on the list that opens, go to the bottom
And click Choose Program / Browse (varies with versions of Windows)
Then navigate to your Program Files folder where the MS Publisher.exe is.
There should be an option 'Always Open with this Program' somewhere.

It gives a list of apps (notepad, paint, explorer, therefore, others I've never heard of (and some of them require purchase). Program files shows MS Publisher DOES NOT EXIST ????

...on a volume that has somehow been unmounted or deleted?

Update: Spent a couple hours on the phone with Microsoft customer service. Turns out that something had removed my Office Suite; they did a remote download and reinstall. It worked, I can now access my files again. Following the panic nightmare of having to recreate all those files, I'm glad I have my annual cardiology checkup today. Yeesh. And thanks for the help!

You need to browse to find it, if it isn't in the list of programs.

Find your Microsoft Office folder. Probably in C: Program Files (you may have two of these - 32 bit and 64 bit - look in both)
Inside it will be a few other folders. I'm using an old Office version, so can't really help you locate it accurately.

The file you are looking for (on my system) is called MSPUB.exe in a folder called OFFICE (number).

Most important, after right clicking, Open With, search for an option that allows you to go searching for the Publisher.

they're currently transferring me to an Office tech.

Wish me luck!

Let us know how you go and don't give them your bank account log-in

Update: Spent a couple hours on the phone with Microsoft customer service. Turns out that something had removed my Office Suite; they did a remote download and reinstall. It worked, I can now access my files again. Following the panic nightmare of having to recreate all those files, I'm glad I have my annual cardiology checkup today. Yeesh. And thanks for the help!