Can a state home take her trust money as an asset after she moves in?

The answer depends on (i) whose money is in the trust and (ii) the terms of the trust, i.e., if it says she has ANY right to get the money, it may be countable as her asset for these purposes. You'll need an attorney to read the trust document and advise you about that.

I don't speak as an expert but I used to work in a government-run health care facility and my guess would be yes, they can withdraw from the trust whatever they usually charge per month that is over the amount they receive from SS and other money, and will continue to do so until the trust is drained.

Not an expert at this either but...
They will take money if she is getting it. If it is still in a trust and it has not been distributed they can not take it. (example, I have my husband listed in my trust it is a Special Needs trust, if I am not yet dead he is not getting the money yet so the facility would not be able to take it. Once I am dead and he starts getting payments it would be used for his care)
But is that not the intent of the money? To provide for her care? Or to provide for her in general? The facility will not take MORE than their rate from the disbursement.
I think it would be best to check with an Elder Lawyer to determine what should be done.
I am sure you will quickly get an expert answer.

mom1952: Do you mean to say "she has to move into a section 8 home?"