Unemployment benefits are not available to everyone who loses his job. While the exact criteria for receiving benefits varies from state to state, in most states a person fired for stealing will be denied benefits, because he was fired for malfeasance. If a person is denied benefits because he was falsely accused of stealing and then fired, he may have to consult an attorney to receive benefits, because an appeals process will likely not help him.
When a person files for unemployment benefits, the state agency that administers the benefits may check with the person's former employer to determine the circumstances under which he left his previous job. An employer who fired an employee for stealing will likely report this to the state unemployment agency. If the state includes laws that prohibit employees fired for theft from receiving benefits, it will be on the employee to prove to the state agency that he was fired for other reasons.
Normally, a person would be able to use an appeals process to contest his denial of benefits. However, the appeals process for benefits generally only looks at the reason why the person was fired. If an employee was fired for theft, then the employee may not actually disagree that this was the reason he was fired. What he disagrees about is whether he should have been fired for this. Therefore the denial will likely stand.
To receive benefits, a person would have to force the employer to change the stated reason for his termination. To do this, the employee may have to consult an employment lawyer familiar with his state's laws. This lawyer will be able to advise him on how he might be able to contest his termination. The lawyer will likely direct his actions at the employer, not at the state agency, as it is the employer who provides a reason for termination.
In addition to receiving benefits, a person who is fired after he is falsely accused of theft at work may be entitled to additional benefits from his employer due to wrongful termination. While the employer may have acted in good faith in firing the employee, if the employer was negligent in its investigation of the case, then the employee may be able to get his job back or receive some additional compensation for his severance.