Is it correct for them to charge my mother for a crime she did not commit although it is her responsibility?

My mother is being accused of taking 4 thousand dollars in cash from her work. She had been given 5 thousand dollars to deposit and put the money in a desk drawer until the person who was making the deposit came to pick it up. No one ever picked up the money, so it was left in the drawer. Next day 4 thousand dollars are missing and my mother was questioned over the matter. They wanted my mom to sign a promissory note stating that she would pay back the money that was lost, my mother did not agree to those terms and left the job and did not go back. They never accused her or pressed charges, about a month later the police came to the house and took her in for questioning a couple of hours later we received a phone call that she had been arrested. How can they charge her with something that they do not have proof of, it could have been taken by anyone in that office. I understand that the cash was her responsibility, but is it her fault it was stolen?