This phrase often carries emotional or moral judgment, implying a fixed nature or inability to change. He may say he's changed, but once a liar, always a liar.
Pro Tip 2/3
Not Literal
It's an expression, not a fact. People can change, but this phrase suggests skepticism towards that change. She returned the stolen money, but people say once a thief, always a thief.
Pro Tip 3/3
Informal Context
Mostly used in casual conversation. It might be inappropriate in formal or sensitive situations. At the reunion, they joked that once a class clown, always a class clown.