Hi Phil, and welcome!
I'm so sorry to hear that your sister lost all her ID information. The TSA understands that these things happen and they have a list of acceptable ID's, which I'm including for you, here: CLICK
As you can see, they also can check publicly available databases to confirm your sister's identity and she should be able to fly. Her birth certificate and expired passport are not considered valid identification for these purposes, but will help find her information in the databases. Her picture ID card as a member of her convent at Notre Dame may be of help, as it contains her picture, but it is not a government issued, photo ID, like a driver's license or state ID card.
It sounds like she will have enough 'evidence' to prove who she is and as I mentioned, they will check the databases to confirm her identity.
My recommendation, under the circumstances, is for her to arrive at the airport about an hour earlier than usual, because this 'extra' step of verifying her identity without a government issued photo ID will take a little longer. She can tell the TSA screener, right away, that she lost all her ID on her trip, so they are aware of the situation and can help her immediately.
I hope all will go well and I wish your sister safe travel!
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