Patient protection in a biopotential amplifier
Suppose you have designed a device. Now you have to review how it can fail. You perform a formal Failure Modes and Effects Analysis (FMEA) to determine what happens when each component fails. 

You know how the patient is connected to the equipment. The patient is likely to be connected to earth.

If you know what happens when each component fails, you can determine what will happen to the patient. For instance, suppose a resistor failing short circuit could lead to excessive current flow through the patient to earth. This is an unacceptable failure effect of the circuit and must be mitigated before the design complies with the standard. The exact methods used to mitigate hazards depend entirely on the circuit design, system design, and intended use. 

Beyond the FMEA, other statistical safety analyses may be required depending on the complexity of the system and its relevant regulatory requirements. In the aircraft systems I work on, the FMEA feeds into a fault tree analysis (and many other documents) that tells you how likely each fault is. The probability of a fault and its associated hazard play into each other. More critical faults are required to have a lower probability of occurrence.

The ultimate goal is to show that, under all foreseeable operating and fault conditions, that there is a very high level of confidence patient will not be exposed to hazardous levels of electrical energy.