That would be skin. Especially old, saggy skin that was once overweight and now is minus the fatty tissue and, therefore, filled with nooks and crannies and pockets too, I would imagine.
Reminds me of old Bill and old Ben sitting outside the nursing home when old Molly streaked, naked, across the yard. Bill said, "Wasn't that Molly?" Ben said, "I believe it was." Bill said, "What was she wearing?" And Ben said, "Darned if I know, but it needed ironing."
The best bit is that pockets were given as gifts, and that pockets coukd be bought ready made. (It seems counterintuitive doesn't it?) But also pockets were stolen. So the original form of pickpocketting was actually stealing the pocket itself. How strange!