When I don't give someone a good-bye hug, it feels like something is missing.
この場合、次のような言い方ができます。
A: Do you feel like anything has changed about you since you came to America?
「アメリカに来てから何か自分が変わったと感じる?」
B: When I don't give someone a good-bye hug, it feels like something is missing.
「さよならのハグをしいないと物足りなく感じる」
to give someone a good-bye hug で「人にさよならのハグをする」
ご参考まで!