What are strategies used when trajectories, which are applied to a robotic joint, are interrupted? Say a robotic arm hits an obstacle, the controller just keeps applying the trajectory. Then at the end, the error gets so large, the torque can get quite strong and damage the robot or snap.
If you have no possibility to detect the obstacle apriori (e.g. with cameras, vicinity sensors...) If you already hit an obstacle and your position error increases, you can only detect the problem by the increasing position error or indirect by the increasing motor current.
Most of the motion controllers, I have seen, have tons of configuration parameters, including an error limit. This limit parameter tell the controller to disable the motor in case of this threshold is exceeded. This is done to protect the robot-hardware itself and also the environment (e.g. a wall, a crate or even an human being).
In the procedure of setting up the robot this parameter is usually tuned, to avoid damage in case of an error but also to avoid false-positive alarms in case of a to small threshold.
As it should be clear my answer is based on a system with a closed loop setup
In 1981 Raibert and Craig wrote a paper Hybrid Position/Force Control of Manipulators which was published in the June 1981 issue of Journal of Dynamic Systems, Measurement, and Control. It was republished in Brady's book Robot Motion: Planning and Control. You can find many similar concepts today, some being called "position and torque control," and others using velocity and/or force variables for the combination. If you are able to sense joint torques (or motor currents), this would be a great approach. If you cannot sense the joint torques, you can use an end effector force/torque sensor. This would work for the scenario in which the robot cannot finish its positioning task when the object being gripped (or the gripper itself) hits an obstacle. It would not, however, detect when an individual arm link encounters an obstacle.