We may be late on this, but we’re hearing about a new flexible battery technology — Lithium-Ceramic — from a Taiwanese company ProLogium (be warned that the page likes to pop up lots of dialogs welcoming you).
The batteries, called FLCB, are flexible and can apparently be made credit-card thin, as this video illustrates:
ProLogium also has posted a video showing how safe and stable FLCB seems to be. (The video is marked “Confidential” but is posted on the company’s public website.)