Flexible Plywood sheet
I saw this instructable a while back on how to cut a flexible ply sheet, the idea is that it can flex in multiple planes at once. I was a bit sceptical and when it came up in conversation again this week I took the opportunity to cut some samples for someone else. The result is a relatively flexible sheet, I wouldn't really call it a super flexible sheet.
I tested it by pressing it down over an object and seeing how well it deformed. I started using 2.7mm poplar plywood, my favourite material that is already lightweight and flexible. It took about 12 minutes to cut a 200x200mm section. It flexes quite well in one plane and with encouragement in the second. I still wanted more so I cut it again in 1.5mm ply and 0.8mm ply. The thinner the ply, the more flexible the sheet. It helps that the 0.8mm stuff is already called flexible ply and can be wrapped around without any cutting.
Given the amount of time it takes to do this kind of cutting it would help to have a very specific purpose in mind. The 0.8mm ply can be encouraged to flex around interesting surfaces so it may just be more beneficial to use that instead.