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For example, if the static friction threshold was broken but then the applied force was lowered below it, would the object keep accelerating?

The question states that a force is accelerating the object to the right, does that mean static friction is irrelevant in every case? The applied force in the problem was less than the max. static friction, but once again, it was stated that "a force is accelerating the object to the right". The kinetic frictional force was well under the applied force.

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Static friction and kinetic friction between two surfaces both involve electrostatic forces, but with different mechanisms which are complicated and are not completely understood even to this day.

However, we do know that once the static friction threshold is passed, the kinetic friction rules and the static friction mechanism is not in play in any way.   If the applied force falls below the kinetic friction force, the object will start to decelerate, but due to its mechanism, the static friction force will not set up again until the object comes to a stop.

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  • $\begingroup$ +1, good answer. Just wanted to add that 'static' friction is defined as acting only when there is no relative motion. Any friction that acts with motion is defined as part of 'kinetic'. $\endgroup$
    – DilithiumMatrix
    Commented Dec 7, 2016 at 15:58
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The question might be referring to rolling motion which requires there to be static friction at the contact point with the ground. The accelerating force must be less than the limiting static friction force otherwise there will be sliding.

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