Criminality is likely the most common reason to be found to be inadmissible to Canada for citizenship purposes. It's possible to apply for criminal rehabilitation.

Although inadmissibility problems arising at the citizenship application stage may be less common than similar issues arising at the permanent residency application stage, the wording of the Immigration and Refugee Protection Act means that even permanent residents can be vulnerable to inadmissibility accusations until their citizenship has been confirmed. In the worst cases, your permanent residency could be at risk, and you might even be issued a removal order from Canada. 

It's important to act quickly at the first hint of inadmissibility being a potential issue in your citizenship application process, so that you can either attempt to straighten out any misunderstanding with the IRCC or prepare yourself to go to the Immigration and Refugee Board to contest a negative citizenship decision.