Her husband is a Permanent resident in the US and he would like to apply for the skilled worker programme in canada. He took the assessment and scored 74. However he wants to take his wife with him also but she is out of status in the US as she overstayed her visitors visa.
Would this affect his application even though he is the principal applicant?
or would his wife have to go back to her original country for him to put her on the application ?
The place you could run into problems is with the medical. If the wife were to get her medical done in the U.S. and then needed follow-up testing, she would be required to go back to the same physician. If she were detained or deported in the interim, she wouldn't be able to go back to that physician and that would kill the application.
Other than that, there's no problem with her being 'out of status' in the U.S.
My point about the medical is that sometimes some follow-up blood work is needed, e.g. If the wife were detained, she would be physically unable to go to the same doctor.
She shouldn't run into problems regarding the FBI record check unless she's actually committed a crime in the U.S. The FBI doesn't (to my knowledge) use the record check as an opportunity to hunt down out of status individuals.