If I am going out to buck logs then I take a bunking saw. Falling saws were designed for falling with two people required and good bucking saws were designed for bucking with one or two people. Good old bucking saws are stiffer and difficult to bend, and the bucking saws that can be purchased new today are simply too stiff to bend hardly at all. Even with falling saws, bending a saw in a loop will sometimes leave you with a bent saw. A saw needs to be straight to work correctly and straightening a bent saw may take several hours of precise hammering.
Saws also do occasionally break when bending to load on a pack animal.
My point, to bend a saw when it is not necessary is an abuse of a fine scarce tool. My saw is packed in an enclosed scabbard that is hung lengthwise just under my calf on one side of the horse and the other equipment is packed on the other side to balance out the load. HDPE is a very tuff lightweight plastic that is used for making many things from cutting boards to Tupperware. It is easy to work with using wood working tools and is relatively inexpensive. The plastic is cut to fit the saw then riveted together.