풀리다 is what happens to something knotted when it comes undone by itself. It covers muscles loosening ([날아갈 듯 가벼워진 어깨] 어깨가 이렇게 풀려서), stress draining away (그러면 스트레스가 이렇게 풀리더라고요), a situation resolving (아마 상황이 좀 쉽게 풀리지 않았을 것 같아요, 이렇게 풀려요 여러분!), and egg dissolving into hot broth (계란이 아주 얇게 풀리거든요). The -게 adverb is mostly 이렇게. 풀다 is you undoing something; 풀리다 is it coming undone.