Historically, jockeys could, and frequently did, remount horses that fell, unseated rider or refused during races, in order to complete the course and collect prize money. Sir Anthony McCoy, for example, famously remounted odds-on favourite, Family Business, to finish alone and win a race at Southwell in January, 2003, in which all seven starters failed to complete the course unscathed.
However, since November, 2009, when the British Horseracing Authority (BHA) introduced new safety rules, jockeys are not allowed to remount horses after the start of a race. Jockeys may remount, with the permission of the racecourse doctor or veterinary surgery, if they are unseated during the preliminaries but, once the race is underway, may only remount, with permission, for the purpose of riding back to the unsaddling enclosure.
Of course, the rule change introduced the possibility of races being declared void in the event of no finishers. Indeed, that eventually famously happened for the first time in a novices’ chase at Towcester in March, 2011; two of four the runners fell at one fence early on in the race and, at the same fence on the second circuit, the favourite refused and unseated his rider, hampering the only remaining runner so badly that he, too, unseated his rider.