This happened in our game last night.  I just want to make sure I handled it in a manner consistent with the rules as written.

Bobby and Jake's characters, having set the false signal fire to draw the naval warship away from pursuit of their ship, are running back across the island to their longboat.  In the dark, they stumble over something that squeals.  A piglet?  But that must mean that there's also...a boar!

So the boar rolls really well, Bobby rolls really badly and brings down the pain.  The boar has lots of bonus dice, plus sharp scary tusks (+1 weapon), and again the boar rolls well and on the very first roll, Bobby is Broken.  Before too long he's emptied all three of his pools, so he can no longer spend from a pool to act.  He hadn't taken above Broken, but since he couldn't act we decided that he had to drop out of BDTP.  He and Jake were sharing Intent, so Jake continued to fight off the boar and eventually succeeded in driving it away.

I couldn't find anything to support this in the text, but it felt right.  I couldn't really see any other option.  Does this seem right to you guys?

Of course, that's how it goes. You only ever get out of BDTP if you or your opponent declines to act. Whether that happens because you can't, or because you choose not to, is immaterial.