You gain zero additional rights by being placed on administrative leave pending the outcome of an investigation. Your employer is not a court of law and you are not a suspect held by the police. You may fully cooperate or refuse to cooperate or anything in between. You have no right to present evidence. Your employer has no legal duty to consider any evidence you might have, even if it exonerates you. If if they know with absolute certainty that you did not do whatever it is you are accused of, you can be fired anyway.
If you are terminated, you have the absolute right to file for unemployment. If your employer cannot show credible evidence of misconduct, and you have enough wages in the lookback period, you will likely be approved for benefits while you look for a new job.