You could use a thin, flexible duffel bag that you can roll up to a compact form.
For example:
This bag has similar capacity to a carry-on when in use. After the flight, you can transfer any items to a larger checked bag and/or trash bin, and the entire bag folds into a smallrelatively thin, flexible disk with the profile of the circle at the end (that's what thatthe horizontal zipper is intended forcloses the bag into its own pocket and holds it in that form). You can roll this up further and fit it in a reasonably large pants pocket, or in/attached to the larger suitcase. Then you can use it again in the future, as many times as you want. (Or you can more easily give it away / throw it away.)