OK, I think I may have answered my own question...before you set it as desktop background, save it in your Favorites. But if you never saved your old desktop background, is there anything you can do?

On an Android phone, anything you save as an icon or a desktop will also be saved in a folder called "Downloads" that's inside the "Gallery" folder. Not sure if that applies to your situation or not.

In windows XP, I'd just save the pic somewhere, then go into the Display properties and use "browse" to select the pic I wanted for the background.

My workflow from Windows 3.11 for Workgroups has been to always save something I found on the web to the hard drive, then point to that location so I'd have it forever. Once the "save as background/desktop/etc" came to browsers I shunned it as witchcraft...mostly.

I do remember a time or two when I was running Windows XP when I had a wallpaper image I snagged from the browser and wanted to keep it (or mail it to someone) and discovered it was hidden in the Application Settings folder so I was able to save it to somewhere a human could find it, then replace it.

Each wallpaper image (desktop background) is saved as a separate image file. If you originally set one up from Windows' default image set when you first got the PC (which you must have - I don't see how it would display otherwise), you can get it back again.
Try exploring C:\WINDOWS\Web\Wallpaper and C:\Documents and Settings\All Users\Documents\My Pictures\Sample Pictures with an image browser such as irfanview (which I wholeheartedly recommend as the best software to view images). You'll probably find it in one of those two locations.
I have my own folder where I save all of my wallpaper images, then I set this in the Desktop Properties dialog box using the Browse button, as DarkForest suggested. A fun thing to do is to use these images as your screensaver. Put all of your nicest photos and drawing files in a folder that you choose (which can be one of the two above, if you remember where it is!). Select the "My Pictures Slideshow" in the Screensaver tab of desktop properties, then tell it which folder to use from the Settings box. Using a slideshow of all your images is a really fun way of seeing these images again.