As someone who has a nanny, I think it is entirely appropriate to contact a reference you trusted and tell them the woman they recommended quit via email with less than 24 hrs before starting and without explanation.
All the hypotheticals of terrible tragedies are first, unlikely, and second, still do not undo the potential harm done by last minute quitting. If she applies for similar jobs in the future, her references should know so that they can extend that as a caveat - she is great with kids but has a history of being unreliable.
It's a job, not a charity. You have responsibilities in a job, even if it isn't with formal written contracts. Her actions put you in a tough spot. What if it caused the employer to miss a crucial meeting and she lost her job? What if my nanny did the same and I had to cancel surgery for my breast cancer patients? This isn't date night babysitting. She acted unprofessionally and in a way that would never be tolerated in the real job world. She absolutely shoul be held accountable an notifying her references (dispassionately, reporting only the facts "FYI, I thought she was great and hired her but she quit by email less than 24 hrs before starting leaving me in quite a lurch") is a GOOD thing that may save someone else from the same situation in the future.
shannon
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Another Queen of the House of Boys:
DS#1 2003
DS#2 my mother's day gift 2012
DH
Mikey, the cat and rhinestone-collared, pink-leashed Schatze, our Rottweiler girl