A word or phrase for something thrown away that is repurposed

For objects, the term for the process is upcycling:

Upcycling, also known as creative reuse, is the process of transforming by-products, waste materials, useless, or unwanted products into new materials or products of better quality and environmental value.

Wikipedia

Note that upcycling has a positive connotation. Depending on your context it might work better to use an adjective: e.g. upcycled materials.

Co-opt is probably as close as you get in English.

divert to or use in a role different from the usual or original one.
"social scientists were co-opted to work with the development agencies"
Oxford Dictionary online:co-opt

But this lacks the discarded part. Usually, whatever was co-opted was filched, more or less.