The primary listing exchange runs it. During the preceding quotation period it publishes an indicative price and imbalance, which updates as orders arrive and is the only visible information about where the stock will reopen. Extensions occur when the indicative price keeps moving or the imbalance cannot be resolved.
For traders the reopening is the one moment in a halted stock where a market-order is genuinely dangerous: it executes at whatever the auction clears, which can be far from the last indicative print.
Example: at 10:41 the indicative is $12.60 with a 400,000 share buy imbalance. Sell orders arrive and the auction clears 2.1M shares at $11.85, well below the last indication a minute earlier.
Related: trading-halt, limit-up-limit-down, t1-halt, opening-auction, closing-auction