How does DC braking stop an AC motor without considering current direction?
Induction motor DC injection braking is like eddy-current braking. DC injection braking is accomplished by disconnecting the AC supply and applying a DC voltage to the stator windings. DC current in the stator windings produces a stationary magnetic field. The motion of the rotor bars through the stationary field produces currents in the rotor that have a resulting magnetic field that opposes the motion that produces it. That is best explained in the Wikipedia eddy current article and the Wikipedia eddy current brake article. 

The torque produced by DC injection braking is moderate to high at high speed, increases to a peak at a lower speed then drops to zero at zero speed. DC injection braking will not hold the rotor stationary. It provides only minimal resistance to slow rotation.

See also: How much DC voltage is needed to brake a 3 triphasic motor?