Lyric discussion by hoppingbunny 

Cover art for Cold Piece lyrics by Jerry Cantrell

I think it's fairly obvious it's about a girl who thinks she can try to change a guy (to "save" him), and the guy's not having it.

Of course I could be way wrong on this, but to me, a "cold piece" makes me think of a gun. Guns are sometimes referred to as 'pieces' so a "cold piece" could be an unused gun kept in a home. I guess he might scare her off with a gun - which is a pretty hilariously absurd notion.

My Interpretation

@hoppingbunny can see where you are coming from, and definitely could be interpreted that way.