Could a co-owner of a house get a 2nd mortgage loan without the other co-owners permission?

I think it depends on how the house is titled. Bring a copy of the deed to a real estate attorney with expertise in the community where the house is to get an expert opinion.

If brother wants to protect his interest in the house, he and sister should establish a trust or limited partnership in which they are joint trustees or joint partners and require both partners/trustees to approve any loans against the house.

Or another option is to sell the house, split the proceeds, and let sister and her husband do whatever they want with their share.

You don't get a 2nd mortgage unless you have a 1st mortgage. Since there is no mortgage on the house now, sister and her husband can borrow. Your brother is not well protected.

But, if they go through legitimate lenders, they will have to have a title policy which will include a search for who is on the deed.

Dam some people have no clue when they answer a question. No they could not take a Mtg without all owner being on the new loan as long as the brother is on the title, no one can take a loan without him knowing.

No.