If your bushings are worn and you're having steering problems, you need to address it before it becomes a safety issue.
Other things to look at would be tie-rod ends (the ends of the rods coming out of the steering rack that turn the wheels) because those can wear out. Also the ball joints, which connect the control arm to the wheel/strut assembly. However, if you had worn balljoints or tie rod ends, you'd likely notice shifty and upredictable steering while driving, not just while braking.
The tension rods stabilize the control arms and are responsible for keeping the wheel in the proper caster alignment. Without the tension rods, the control arms are able to wobble back and forth, and so therefore so are the front wheels. For example, when you brake, the vehicle weight shifts forward over and the control arm and wheel would want to shift back in the wheel well. The tension rods are what prevents this, as they connect the control arms to large brackets bolted to the front of the frame of the car. If the bushings are worn significantly, the steering becomes unreliable when the vehicles weight shifts front/back or when driving over bumpy roads.
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1985 300ZX n/a
See my Z project