查了一下OED,dead做副词有个义项是“to extremity, ‘to death’ (as dead run, dead tired)”,到了极点,'到死'(如死跑,死累),所以这里的dead应该依然还是“死”的意思,依然是做副词。keeled over dead就是摔到了极点,当然也就是摔死了。因此,Jasper keeled over dead.=Jasper keeled over to death.=Jasper keeled over and died.
这样理解大约是正确的吧!