To be disqualified from a race means that the player fails to finish the race even though all the other racers have finished the race. When the player is disqualified, their vehicle is wrecked and they earn the least amount or no amount of credits possible.
There are some reported instances on the Android, iOS and Windows platforms where players have been disqualified from Time Limited Events, Cups and occasionally regular Multiplayer races. This is the result of a bug that kicks in at the very beginning of the race, causing one or more players' vehicles to explode and wreck before leaving the starting grid and immediately disqualifying them.
The affected players are unable to continue, but can still spectate the rest of the race if there are any survivors continuing the race.
Under normal circumstances, like simply not finishing any race type or wrecking in a Flawless race, the player cannot spectate the rest of the race as it ends at the point of disqualification.
It is also possible to get disqualified (during Event races) by pausing the game during a race for a prolonged time.