Consider languages like Japanese, ASL and others which have word orders governed not by grammatical relations, but by Topic/Comment structure.
Seems like it should mean "I am an eel", but in the context where everybody is ordering their main courses in turn, it's natural (for humans) to parse it as "As for me, [the order] is eel." It's because of the adposition は. If I say 私がえびです, then it unambiguously means "I am an eel".
Or in British Sign Language, to say "who is that man?" we say "man there who?" Since the man is the topic, (who we are asking about).
Have any statistical MT models tried to deal with this kind of thing when translating from a language that does not do this to a language that does? My intuition is that those IBM alignment models don't map to this phenomenon easily, but I don't know that for sure. If there have been attempts to identify a topic in a sentence, and then front it or otherwise mark it, how has that worked?