This is actually something I've pondered, but not with a starfish, but, say, a Venber. Remember, the creatures from #25 that melted if the temperature got above freezing? Could they even be acquired/morphed? And, if you morphed one, wouldn't your morphed parts melt while you were morphing? As in, any Venber parts that were touching human parts, would get warmed up and melt, and your body would basically fall apart in mid-morph.
I suppose that one could argue that it's a bit of a moot point, since you couldn't really acquire a Venber, anyway (since the very act of touching it might kill it). Still, it's something I've always wondered.
To answer the starfish question, though, I think they've actually done things while morphing that are somewhat similar to that. For example, while morphing dolphin, their wind-pipes will briefly close off when the blowhole forms. My guess is, that the morphing happens quickly enough, that any potentially-fatal mid-morph doesn't last long enough to actually kill you.