Orders must be marked long, short, or short exempt. A locate is required before a short. Fails must be closed out within set deadlines, faster for a threshold-securities-list name. And the alternative uptick rule, rule 201, applies when a stock falls 10% from the prior close: for the rest of that day and the next, short sales may only execute at a price above the national best bid.
That last piece is the one traders encounter directly. On a hard down day short orders start getting rejected or queued because they cannot legally take the bid.
Example: a stock closes at $20 and trades to $17.95, a 10.25% fall. The circuit breaker arms. With the best bid at $17.90, a short sell order may only fill at $17.91 or higher.
Related: locate-requirement, fail-to-deliver, threshold-securities-list, short-selling, naked-short-selling