glipper puts a little icon in your system tray to keep a list of your clipboard (cut/copy) and your primary selection (which is what gets pasted when you click in a text editor [or wherever] with your middle mouse button). A welcome side-effect is that it takes ownership of what you cut/copy or select... so you can past it even after closing the application that you cut/copied or selected it in.

Included in some Puppies under PuppyMenu > Desktop > Glipper clipboard manager

Otherwise install an appropriate software package:

Glipper 1.0 'lite' PET post

Clipboard

Glipper thread