You want to minimize weight and maximize surface area, as well as increase impact time. If you're given the option to hold onto a giant piece of extra-strong pinkboard with grip handles, that'd be ideal.
Unfortunately, this debris usually means you give up control, so it's a tradeoff you have to make. If you're over the middle of the ocean and two miles of lateral movement won't help you, by all means stay with your debris. But if you're falling over a mid-sized city, you have lots of things beneath you: buildings with glass skylights, piles of snow, and occasional trees. Landing on any of these things is far better than staying with whatever object you've got a hold of.
If you are hanging onto a piece of debris, do you want to try to let go of it before impact? I'm assuming it's something with more drag than you, so presumably you're hanging under rather than surfing on it..
Although that's another interesting question. Maybe there's debris that wouldn't be particularly useful in slowing your descent, but could be useful to break your fall on impact... I can't immediately think of something that would be sufficiently good at that that it would be worth carrying with you though.
They do have inflatable life rafts. Might make a decent parachute too, but given their size would be tough to get it oriented and hang on.
Inflatable life jackets too, but those probably wouldn't be substantial enough to make much difference. (Although probably better than nothing if you could manage to actually don and inflate one while falling.)
