Make a point of touching base with each person who works under your supervision. Ask them if there is anything you could do that could be helpful to them or improve the way they are able to do their job. Be aware of the number of times you receive a suggestion that may be small and simple, but that you may not have thought of on your own.
Doing this exercise routinely with each worker can help prepare you to act when one of them may be emotionally distressed. Rather than trying to gather all this information during a stressful time, you will have built a base of knowledge in advance, and it should be much easier to understand and communicate with a worker in an emotionally charged situation.