If you have sole (or joint) care for minor children when you (or both, or the survivor, of you) die, then you should have given advance consideration both as to who will take over that care, as seamlessly as possible, and as to what financial provision you might make. This is the appointment of ‘guardians’ who usually (though not necessarily) will be appointed under the Will, when they are called ‘testamentary guardians’.
For obvious reasons careful advance thought should be given to this, along with focussed discussions with the chosen person/people. Not necessarily so that your children will know who they are (after all, we don’t want to raise in their young minds the terror of the possibility of your unexpected death), but so that if the unexpected should happen the children will feel comfortable with whom they go to live.
Each circumstance will be different, though the Guardian(s) could be a relative or a close friend, perhaps someone who has a child or children of similar age/ages. With them you should have discussed financial provision in advance, may be taking out term life assurance to provide for that. The Guardian(s) should be aware of your values and how you would like your children brought up and/or of the special needs of a particular child. And you will discuss with them how they will fit in with the Guardian’s own family. That said, once the move is made, you will have to trust the Guardian(s) to make decisions that are in the best interests of your child/children.
And then what would happen if when you die you have direct personal responsibility for a dependent relative, may be one living with you or close by whom you look after? The same general principles would apply.
As also with pets, who will doubt take your death hard too. Clear instructions should be left for the nominated person(s), together with relevant details including any insurance policies, all as noted in the Critical Checklist in my Book.