What does it mean when your auto insurance company wants to put your policy under indemnity?

I don't believe it was explained to you correctly. You probably received a notice of cancellation from your insurance company and someone in the office told you they were going to put you in their indemnity company. Many direct writer insurance companies have a second company that they either have a completely different name or it may have a similar name to the main company. Allstate for instance has Allstate Insurance Company and Allstate Indemnity Insurance for people who have had too many claims or tickets and no longer fit the preferred companies guidelines.