My own google-fu tells me that both of those searches are likely to be pretty poor - using the word "fall" instead of "collapse" is likely to snap up quite a fe

My own google-fu tells me that both of those searches are likely to be pretty poor - using the word "fall" instead of "collapse" is likely to snap up quite a few weird results about autumn tourism in italy and including "empire" in the second query feels likely to get you a batch of other poor results (like, for instance, the collapse of Russia commonly known as the third roman empire). Personally I'd suggest "collapse of rome" which does deliver you a rich embedded result specific to the fall of rome. I agree that Google's search parsing peaked a while back though, it seems to be getting weaker and weaker and now partially relies on the fact that search term autocompletion on mobile devices will supplement it by helping present an array of options near what you might want.