This is not true. No one can be elected vice-president who is not qualified to be president (12A), and someone who is doesn't meet 22A requirements is not qualified. But there is actually a real hack to skirt 22A, but just not that way.
I don't understand your toot because there is too much ambiguity in its content. What is: "next election", "take over again", "one ticket left"?
If someone is not eligible to be elected president, then they are not eligible to be elected vice president because of the 12th Amendment, "...no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President..."