She's gonna hate being the namesake of such a homely thing, but Velouria, of Lovely Bicycle had a great suggestion a couple of weeks ago for using pairs of plastic bags in tandem as panniers.
The CSA season started for me last week, and I completely forgot about it until I got to work, which meant I only had my normal small-ish leather daily bag . In the past I've resorted to making temporary panniers out of boxes or baskets, secured by rack straps, but this time I decided to use "V-Panniers"
These were a bit hampered by the fact that I had my normal bag on the left side, and the bag just sitting on top of it. I put the heavier bag on that side so that it would be partially supported.
I put the knotted portion under the "rat trap" and then latched it down with a lock and rack straps.
Bottom line, it was fine for a couple of Kolrhabi and a bunch of bulky but light greens, but I'm not sure I'd trust it with heavy stuff like cans of tomatoes or peanut butter. Not a bad solution though for an emergency! Necessity is indeed the mother of invention.