A 'broken toy' is a synonym for fuck-up, loser, or wreck. Broken toys tend to be people with a history of psychological trauma and a propensity for drug use and reckless behavior.
More specifically, broken toys can refer to women who are fragile or easily manipulated. Some men aim only for broken toys, whether out of sadistic glee, the ease with which they'll jump into bed with somebody, or a foolish and altruistic desire to fix them.
R: Man, this party is full of broken toys.
S: You gonna game on any of them?
R: Shit, that'd be like shooting fish in a barrel.
Amy Winehouse is a pretty seriously broken toy.