I've seen it translated in the context of The Cure "Disintegration" song as "a partner". Translation by polish journalist Tomasz Beksinski.
"...it starts the need to just let go my party piece" means - to let go (resign) of my girlfriend (a partner)
To run a piece on a girl can mean one of two things: to have sex with a girl in exchange for money, drugs, or whatever they decide to exchange.
To run piece on a girl can also mean: to con or steal from her in plain sight without her knowledge, especially if she is in debt to someone
I'll hit you up later but first I have to run a piece on a girl who needs some Boi or tonight, but she don't have any money.
Vagina. As is ‘snatch’ alone, but used similarly to ‘ring piece’ for anus.
Take off your panties and let me see your snatch piece.
An extremely used or dirty bowl or pipe used for the consumption of a combustable substance such as marijuana.
"Put that butt piece away, we'll use my glass man, I just cleaned it."
A classic navy blazer, white dress shirt, and khakis.
I can wear my Irish 3 piece suit to grad party’s, funerals, formals, or court.
When a girl (or whomever) is disappointed to find her man has a small penis.
“I hooked up with Patrick last night. Got four tenders in my six piece.”
Reese's pieces that are made out of horse.
These heese's pieces are delicious and taste exactly like if not better than the real ones.