a business is owned by two people. One of the co-owners dies. The business had a loan secured by both owners. The bank found out that one of the co-owners dies and now wants the surviving spouse of the deceased co-owner to sign a guaranty or the bank will "call" the loan.

What can the surviving spouse of the deceased co-owner do? Is there an obligation for her to sign a guaranty on a business that she doesnt run? The surviving co-owner doesnt want to sign it.

The surviving spouse cannot in anyway be compelled to sign something against her will. That would be illegal and constitute a violation with her contractual rights. It is like giving forcing someone to drive when fairly he cannot.
On that score, there cannot be an obligation to sign, especially when the same amounts to creating liability.
The bank may some other alternatives, not just by compelling someone to subscribe into an undertaking that is obviously foreign to the subject. Fairly it is not viable.
Besides, the surviving co-owner, on his side may not like to deal with the surviving spouse of the deceased co-owner. Mere speculation though.

The surviving co-owner may refuse to sign, that’s it.
Peril for calling out of the loan, though imminent, confer with the bank and ask for another accommodation.

If the surviving spouse doesnt sign the loan guarantee, the bank is claiming that they will call the loan. So she is in a bad position....and she cant refinance in this market.

Doesnt look like she has any real choice

Yeah, no real choice. Possibly,ask for another accommodation with the bank. If not viable, concede.