How do you deal with the unexpected in your Business?

We all juggle in our lives, but how do you manage when the unexpected occurs in your business? I don't mean technical issues, but personal issues.

As a Virtual Assistant, I pride myself on my time management skills and organisation. I always meet my deadlines, whether self-imposed or set by the client. The majority of my work is time sensitive and requires rapid responses.
This week I had my work plan sorted, or so I thought. What I hadn't factored into the equation was my teenage daughter coming home from school very unwell. Usually, we get on with it - go to the chemist or the GP, but unfortunately on this occasion she needed to go to A&E. Three visits later, she is finally on the mend, I am a little greyer and certainly we are both exhausted. As a mum, the priority is always my daughter. My clients were understanding and all of them have checked back to see how everything worked out.

While sitting in A&E it made me think about what I need to do when I can't work.  I have never been a fan of having work emails on my phone, but I did have enough time to add them, just in case I needed to work or notify my clients.
For the first time ever, I was unable to meet a deadline - to write an editorial for one of my clients. However, I was able to email him and explain why. I promised to get it to him by the following lunchtime and made the deadline with four minutes to spare!

Do you have a contingency plan?

Is there someone you can hand over to in an emergency?

Mine is in my head, although admittedly that relies on memory and being able to do it myself.

One of my clients has gone further - she has a written plan (locked away securely) in the event that she is incapacitated or worst case scenario dies. It involves details for her family of who to contact regarding her business. As her VA I am one of the two people she has identified and then we will take care of the business side - notifying clients etc.
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We all tend to rely on family, but is it fair when your family are stressed to expect them to deal effectively with your business? Perhaps like a will, where we identify executors, we need to identify business executors to notify our clients in the event we are unable to work, and lodge the plan with them so they can follow our instructions. Obviously, there are GDPR implications, but storing it in a secure electronic format can overcome these.