No personal information or insurance exchanged in minor car accident?

Will the person whose car had minor accident ,claim for the accident with no personal information or insurancee details exchanged between the two drivers?

Your question is vague but if I understand it correctly, how can we know what the other person will or will not do? How do you know that they didn't record your license plate number ? Protect yourself and simply report this to your insurance company and have them "sit on it" in case a claim against you may be filed with them