I don't often bring back more than I leave with, but I often carry gifts from the USA to give to friends in other countries. (BTW, I learned a long time ago to check the bag containing the gifts, not the bag containing my own stuff!) For this purpose, I use the ProSpirit Small 20" Duffel Athletic Gear Bag . It's sturdy enough to check, yet still folds up small enough to fit in my carry-on bag. I've been using it for the better part of a decade, and it continues to hold up very well.

It shows unavailable from Amazon, but I believe that I actually purchased it from Target. The closest match that I see now at Target is the $20 J World Buena Folding Duffel Bag. Similar size, same concept, but I don't know how it would hold up over time.

ETA: When I pack gifts into my duffel, I usually put them in old Amazon shipping boxes and then put these inside the duffel bag. That gives the duffel bag some shape and also protects the items inside. If you're using it to carry items home, you might consider asking retail stores for small, spare cardboard boxes that they are going to recycle.