PSE crashes every time I try to add border to outside of an image.

I don't know what is the cause of the crash, but anyway you can't add a stroke outside of the image, only inside.

Also you could try trashing the prefs and let us know if that makes any difference.

From the menu go to:

Adobe Photoshop Elements 2020 Editor >> Preferences >> General

Click the button to reset prefs on next launch and click OK

Quit & re-start the application

Or the menu button for your version if not using 2020

It will help us to answer your question if you could provide the exact version number you have installed and details of your operating system e.g.
• MacOS Mojave (10.14) Catalina (10.15)
• Adobe Photoshop Elements Version: 18 (2020)
You can find this from your application menu:
Help >> System Info