If a cyclist fails to complete a stage of Tour de France because of injury or something else, but is ready again for the next stage, is he allowed to continue? If yes, does he receive some sort of time penalty for failing to complete the stage?
I believe that under the following regulation, a rider who does not finish a stage may continue in the next stage, only if the incident occurred in the last 3 km.
Chapter VI STAGE RACES (N)
In the case of a duly noted fall, puncture or mechanical incident in the last three kilometers of a road race stage, the rider or riders involved shall be credited with the time of the rider or riders in whose company they were riding at the moment of the accident. His or their placing shall be determined by the order in which he or they actually cross the finishing line.
If, as the result of a duly noted fall in the last three kilometers, a rider cannot cross the finishing line, he shall be placed last in the stage and credited with the time of the rider or riders in whose company he was riding at the time of the accident. (text modified on 1.01.05; 1.10.11; 1.02.12).
No, the cyclists are not allowed to get back on the bike for the next stage if they do not finish. This has as a consequence that the cyclists continue with very heavy injuries just after a crash, because they hope that tomorrow will be better. (For example, Dutch cyclist Wout Poels, continued racing for 10km after Fridays huge crash, but is now still in the intensive care in a French hospital with torn spleen and kidney and three broken bones in his chest)
Also, I found this article ( http://www.uci.ch/includes/asp/getTarget.asp?type=FILE&id=34028 ) on the UCI website.
2.6.026 A rider dropping out of the race may not compete in any other cycling events for the duration of the stage race that he abandoned, on pain of a 15 day suspension and a fine of CHF 200 to 1,000. After consulting the event directors and the president of the commissaires panel, the UCI may, how- ever, grant exceptions at the request of a rider and with the agreement of his sports director.
In addition to what was said by Bernhard, the Tour de France uses a "Voiture-balai" which translates to a "Broom Truck/Car" (from Wiki). I've been to the Tour a few times and you see the truck at the end, about 30-45 minutes behind the peloton depending on the stage (flat or mountains). This is more of a traditional thing as the Broom Truck has been around since 1910.
It's job is to "sweep" the riders that are far behind the peloton, be it due to injuries or just exhaustion.