If somebody withholds taxes they are required to report that both to the US Government and to the individual whose taxes were withheld.
Brokers are not generally required to withhold taxes arising from the sale of stock and when they do it's called "backup withholding" and they are required to report that on the 1099-B. The exercise of NQSOs requires that the former employer issue a W-2 which reports the compensation created by the exercise and also the taxes withheld. The way that generally is handled, mechanically, is that the portion of the proceeds of the sale designated as "cash for taxes" is passed back to the employer, who then pays the government,
Call the broker and ask what happened to the amount of proceeds earmarked as being for taxes. I'd be surprised if it wasn't sent on to the employer. Follow the money.
