If the drawbar on the trailing end of a car is pulled out, then the head end of the train can be pulled ahead and the damaged car set out at the first available trailing point switch. The head end of the train is then backed up so it can pick up the rest of its train.
If the drawbar on the leading end of a car is pulled out, it's a real mess. If a heavy chain is available, then it might be possible to connect to the damaged car using the chain. Using the front part of the train, the damaged car is cut away from the rest of the train. The damaged car is then set out as in the previous paragraph. The head end of the train then goes back to pick up the rear of the train. The easier method is if there's a mechanical trouble truck available that can deal with the problem right where it happened. But, of course, you have to wait for them to get there.
In any case, if the damaged drawbar is fouling the track, it must be moved before the train can be moved. Back in the day when you had at least a four-man crew, they could do that by hand. These days, with often only a two-man crew, you'd have to wait for help to arrive.
jb