Twenty-second Amendment to the United States Constitution
As worded, the primary focus of the 22nd Amendment is on limiting individuals twice elected to the presidency from being elected again. Due to this, several issues could be raised regarding the amendment's meaning and application, especially in relation to the 12th Amendment, ratified in 1804, which states, "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States". While it is clear that under the 12th Amendment the original constitutional qualifications of age, citizenship, and residency apply to both the president and vice president, it is unclear whether someone who is ineligible to be elected president could be elected vice president. Because of this apparent ambiguity, there may be a loophole in the 22nd Amendment whereby a two-term former-president could be elected vice president and then succeed to the presidency as a result of the incumbent's death, resignation, or removal from office (or even succeed to the presidency from some other stated office in the presidential line of succession).
Twelfth Amendment to the United States Constitution
The Twelfth Amendment explicitly states the also apply to being Vice President. It is unclear whether a two-term president could later serve as Vice President. Some argue that the Twenty-second Amendment and Twelfth Amendment both bar any two-term president from later serving as Vice President as well as from succeeding to the presidency from any point in the United States presidential line of succession. Others contend that the Twelfth Amendment concerns qualification for "service", while the Twenty-second Amendment concerns qualifications for "election", and thus a former two-term president is still eligible to "serve" as Vice President. The applicability of this distinction has not been tested, as no former president has ever sought the vice presidency, and thus the courts have never been required to make a judgment regarding the matter. Hillary Clinton said during her 2016 candidacy that she considered naming Bill Clinton as her Vice President, but was advised it would be unconstitutional.