fold like a cheap suitcase

Collapse easily. Expensive luggage was made, as now, from well-constructed leather or fabric. Cheap ones used to be made of cardboard with little or no structural reinforcement, not very sturdy especially when manhandled by baggage handlers or hotel porters. A sports team with no defense or a poker player with a losing hand would both fold like a cheap suitcase. You'd also hear “fold like a cheap suit,” but since fabric folds easily, whether it's cashmere or polyester, “suitcase” presents a better connotation of a losing proposition.