I have heard of something call titanium foil. It is probably more expensive than plain old aluminum, but possibly it might stand up better to folding. I have no experience with the material at all, so this is rampant speculation.
I bought 11.75-in. x 12-in. piece some months back from
here to test as alternative to Al foil. $15 + shipping (less 10% discount for active duty/veterans). Too many other projects, so haven't played with it yet.
I asked questions before purchase about durability/folding. The reply: "The Ti foil is much thicker than Al foil... it will not tear. Repeated folding will cause it to work harden and break. You want to roll up the Ti foil. This is the same foil that we make the Ti stove pipes out of (0.005" thick). You will have trouble poking a hole in the Ti foil with a nail."
So, still needs TLC like aluminum foil when comes to folding; but nevertheless an improvement (albeit a pricey improvement) if carried rolled as suggested, with expectation that in emergency use, would be fashioned into cup/cooking vessel and left that way (not repeatedly folded/unfolded). Warning: edges are like a razor blade; in use, would have to be crimped over.
Finally, for Al foil,
3M High Temperature Aluminum Foil Tape will work as improvised patch up to 600 degrees (prolonged exposure to open flame could be a problem, though data sheet says flame resistant).