If you are predicting then simply go ahead with the application submission as usual. Later if anythiing changes then you will need to inform CiC. Even you apply for one parent to come to Canada as PR but other parent goes through any situation change, still you will need to inform CiC about that situation change of other parent. Now about false case being registered, that will be mentioned in PCC report by respective govt. office who checks and provided PCC as PCC checks and provide all those information in PCC.