What happens when you run out of filament or filament jams mid print?

Over the past week or so, I had three separate instances where I woke in the morning to check on an overnight print only to find that I had a filament jam (twice) or ran out of filament (once) in the middle of the night. I just groaned, threw the parts in the scrap bin and started over.

However, an (obvious) solution just occured to me. Take the printed part, measure z-height. Then take the model and remove the z-height that has already been printed. Print the new short model and glue to what's already been started.

This probably is not a reasonable solutions for all models and materials, but for ABS that is going to be vapor polished at the end, it should work great.