I save almost everything. I got the second place ribbon for viewers choice for my crazy crumb quilt. Started in the middle with a 5 sided black piece and added all around until it was 8.5 inches. Sashed that with black with 2 inch corner stones made of at least 3 pieces. Some were 8 to 11 pieces. Border pieces were a 1/2 inch strip pieced in many shades of red, then 6 inch piano keys of various widths, all pieced. I used what I had.
I try to save things flat. Strips go into a long candle box and other things go into boxes in such a manner that they do not get too wrinkled. Makes going back to use them much more soothing.
I will save even 1/2 inch pieces if they are an outstanding color. When working with such small stuff, I use 1/8 inch seams. I've made at least 3 confetti quilts using trash fabric for the foundation. No tearing of paper. Old bed sheets, bed skirts, thin fabric, etc. work for the foundation pieces. I have a box for those pieces in "The Closet".