The act of playing up the your level of poverty verbally to excuse yourself or make yourself look worse off than you are. A person who does this is known as a poor-mouth or the act itself is called poor-mouths or poor-mouthing.
He poor-mouths that he couldn't pay the bill, when he just bought a brand new lexus.
To whine and complain that you don't have much money, that you're destitute from other expenses etc. when negotiating for goods or services when, in reality, you're loaded and much better off than the person you're haggling with.
"Don't let him poormouth you into doing that job for half price. He's a millionaire a couple times over."