There are, more or less, debates about Trump impeachment. Assume Trump to be fired, but at the same time vice president misses presidential qualifications.
Who is responsible for the executive?
There's no reason to believe the normal line of succession wouldn't be followed, so the next person would be the Speaker of the House, Paul Ryan. The only position in the line of succession that is currently filled by a person ineligible to become President is the Secretary of Transportation. Elaine Chao, the Secretary of Transportation, was born in Taiwan.
The premise of the question is flawed, because the Vice President can't miss the qualifications to be President. Reference the 12th Amendment to the Constitution:
...But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.
- Be a natural-born U.S. citizen
- Be at least 35 years old
- Have resided in the U.S. at least 14 years