You have to be careful using terminology such as "once clock has started" to determine correctable error or not. Suppose in your play there were 4 minutes left, rather than .4 seconds and somehow the officials don't award the free throws (which would be quite an error since they would have been shooting the one and one bonus up to that point). Instead the ball is put in play with a throw in, whereby the clock DOES start. While the ball is live, say being brought up the floor, the table sounds the horn to alert the officials to the error. Play is stopped and the free throws are now shot. Just because the clock has run does not mean, in this situation, that the error cannot be corrected.