Can I apply for FAFSA when these are the circumstances?

Yes, you can file as @kelsmom pointed out.

If you put $0 for income, you will surely be selected for verification. The colleges will justifiably want to know how your family paid day to day living expenses with no income at all. So be prepared to provide this information.

@kelsmom wouldn’t this applicant still need to list any income earned? Even if they didn’t file taxes?