After several frustrating hours of working with the client, several online sources, and my web host, we managed to solve this issue. Unfortunately, the client still doesn't really know what she did to accidentally delete the folder.
THE SOLUTION was that (a) the deleted folders were in HIDDEN folders. I could see these folders in CPannel File Manager by clicking on the Settings cog and checking the "Show hidden files" checkbox. All the hidden folders had their names start with a period. I took a screen shot of these folders and sent it to the client, who said, "These are the folders I was looking for!" And then (b) In RoundCube (that IS the topic of this board, right?), we went to SETTINGS, then clicked on FOLDERS, then we found an ARCHIVE folder and clicked on that, and there were the deleted folders! WOO! At that point, (c) we created a new folder called STORAGE, which I checked and verified we could see from the EMAIL tab of RoundCube, then (back in Settings>Folders) I dragged the target folders from ARCHIVE to STORAGE, and Presto!
The client now has her accidentally deleted folders back, and can once again see all the critical emails she thought she had lost.
Maybe this information will help someone else.