Posting the following because I've not seen it mentioned. For context, this pertains to an Ivy programme.
A trusted advisor who's in a position to know told me that now is the time to get all assurances in writing, just in case (even though, as someone mentioned somewhere, jumping into the ring to challenge withdrawals of offers would be a very difficult strategy). Before I accepted my offer, I emailed the department to get written confirmation that everything we were being offered would hold. (I phrased this politely and as tactfully as I could! It helps to say something like 'this is my understanding of the situation; could you let me know if I'm mistaken in any way?') The TL;DR is that I did get that written confirmation, so things look good.
The details, because I think they're helpful points for identifying what should count as a good response and what we should be more wary about:
My point of contact with the dept replied promptly to say that, to the best of her/his understanding, my appraisal of the situation was correct. (This is good – already one step in the direction of a written confirmation)
This faculty member also copied in the DGS and the Dept Chair and told me that s/he had asked them to provide any further guidance they could on the matter. The Chair had also decided to ask the School administration for more information. (Taking all this in good faith, this is even better – the cc'ed faculty members are in a better position to know.)
After not hearing back for a week or so, I politely emailed again to ask for updates. Faculty member replied saying it was an affirmative from both the DGS and Chair. (Great ending – for now.)
Fwiw (also haven't seen people mention this), I'd take tenured faculty's opinions of the funding situation with a pinch of salt and take my pointers from tenure-track / non-tenure-track faculty members any day. At least in my limited experience, the former may be well-meaning, but often too chirpy and unrealistically optimistic about things like funding. Again, they may mean well and I appreciate that, but I like it when my advice comes with real, grounded assessments of reality!