You have to put the information, even if you can't validate it because by hiding past employment history you are mis-representing.
Also, it appears that after an ITA you need to provide reference letters for your spouse's work history, even if you don't receive points for that either.
This is obviously not a new situation. If CIC refused anyone who worked for a company that had closed, then they would need to change the eligibility requirements to exclude anyone who had worked for a company that went bust.
If you can provide pay stubs/copies of contracts etc with a letter of explanation that should suffice. If not, probably best to look for another country with a most logical system.