Simply ejected
There comes a point where the extra velocity you could gain by using the escape rocket's thrust is offset by the energy required to carry the extra mass into orbit. Every American system that used launch escape rockets simply ejected them.
It's possible they could've fired them and used their thrust to help pull the stack but then you'd have to carefully choose when to blow the explosive bolts so the LES would fly clear before it ran out of thrust. Those LES rocket engines only fired for a few seconds so I don't know if the added thrust would've justified the extra risk. While not positive, I suspect the Russians also jettison their LES stacks.