I think you heard a part of a song.:) It must be "해져" in Korean, meaning 'getting' or 'to get + adjectives'. here are some examples, 피곤+해지다. I get tired. 익숙+해지다. I get used to something. for past form, 피곤+해졌다. I got tired. 익숙+해졌다. I got used to it. also, '피곤+해져(haejyeo)가다' can be 'I am getting tired'. '익숙+해져(haejyeo)가다' - 'I am getting used to something'. in here, placing '해져가다' before nouns, it becomes '해져가는' just putting '는' instead of '다'. for example, 익숙+해져(haejyeo)가는+나(noun) 익숙+해져(haejyeo)가는+우리(noun) as you can see it, 'haejyeo' is a particle of phrases or expressions. 'haejyeo' itself will not work.