I think it's similar to adverb in English.
ex) 조용=silence, 조용히=silently. 정확=exactness, 정확히=exactly
'안녕히' is also adverb but it's not frequently used alone. I think it means an adverb version of 'take care'
'안녕히가세요' seems to me like sort of idiomatic phrase. It means 'see you! bye! take care!'