"Even the dog refused to eat it" - As even is an adverb here, what exactly is it modifying?
Solution 1:
While adverbs do not modify nouns, they do modify noun phrases:
Probably the best basketball player of all time, Michael Jordan surely has earned his place in the baseketball hall of fame.
When adverbs are modifying noun phrases, it's not possible to put a commma beteween the the noun phrase and the adverb preceding it:
*Almost, the whole movie was boring.
Almost the whole movie was boring.
In the example given, even seems to be modifying the noun phrase the dog as inserting a comma makes it ungrammatical:
*Even, the dog refused to eat it.
Surprisingly, the dog refused to eat it.
Surprisingly, on the other hand, would be an adjunct modifying the whole clause, and hence we could insert a comma.