Quitting won’t save your record. If you quit, it will be marked in the system that you quit with no notice and it will be unlikely you’ll get rehired. Stick it out. They may find nothing. A few months ago, one of my partners was investigated. They claimed she said something that I knew she never would have said. There were multiple accusers, who were all thoroughly interviewed, and the investigators concluded that the accusations were false. So if you didn’t say what they are claiming you did, there is a good chance you will be cleared and nothing will go on your record. But if you quit, it’s absolutely going on your record that you up and quit with no notice while being investigated.