It is a classic "it depends" situation. First and foremost, you will be taken care of. All decisions will be in your best interest as a person before how they impact the program or your participation. In the event of a medical emergency that you suffer, there is a full hospital on base and you will receive excellent care. If the recovery limits your ability to participate - that is handled as a secondary matter and only fully addressed once the medical emergency is overcome.
If there is a medical emergency for a family member, you can be notified. If you wanted to depart to attend the funeral or go be with family, a discussion would happen and your options would be presented. Should the leave of absence occur in such a way that you could limit the impact to a Sunday (personal day), it is realistic that you could do what you need and then resume training.
Regardless of the emergency, you will be cared for and options will be presented. Some options have consequences like removal from the program. You will be informed, but are considered an adult who can make life decisions for yourself and possibly for the first time in your life - you get to make those choices.