If you are making a first party claim, going through your own Collision coverage, for the damages you sustained due to being rear ended in an accident than you will owe the deductible associated with this portion of your policy.
Deductibles are not dependent on if you are at-fault or not at-fault in an accident. They are normally due as long as you use your own Physical Damage coverages to make a claim. There may be a few exceptions (for example for windshield claims in a few states) where the insurance company waives the deductible but usually you have to pay it out before your insurance provider will pay for repairs over the cost of your deductible amount.
It sounds as if in your situation you contacted the at-fault party's insurance company to make a claim however since the other party did not contact their insurer and there was not a police report or crash report taken at the scene their insurance company would not accept liability for their insured. You then turned to your insurance company to make a Collision claim for the damages you received in the accident.
When an insurance company pays out on a claim that they believe was another party's fault they may subrogate with the other party or the other driver's insurance company for the monies they paid out on the claim that was not their policyholder's fault. In this instance your insurance carrier would only be paying you less than $50 so it is unlikely they would go after the other party to recoup this since the cost of the manpower to find the person, send letters, take them to court if necessary would probably be more than this amount they paid out on the claim.
If they did subrogate with the other party than normally you could ask your insurance company to also try to recoup your deductible amount as part of their process. Many insurers will try to do this but it can be time consuming and there is no guarantee your money will be received by the insurance company to return to you.
Since you would only get $32.50 from your insurance company if you went ahead with the claim you may instead want to just pay out of pocket for the repairs of $500 plus and then take the at-fault party who rear-ended you to court to seek a judgment against them for the cost of your repairs. This way you would be able to seek the whole amount of the repairs and you would not have a claim on your insurance record for this incident which depending upon your state's laws and insurance company's rating system may affect your future car insurance rates.