I use a generic folding cane sometimes when I am off the bike. I had used 1 velcro strap and 2 bungee cords to secure this to the rack on the back of my road bike, or had put my rack trunk on, and had the cane mostly inside rack trunk, with some of it sticking out the zippered compartment. When my husband and I bike together, he sometimes put my cane in his rack trunk.
He bought me a seatpost-mounted rack with a trunk bag
TopeakŪ Cycling Accessories ? Products - RX TrunkBag EX and I can put my folding cane inside the elastic strap on the top.