At the time of his death in exile in the United States, he was the oldest member of the College of Cardinals, to which he was secretly appointed by Pope John Paul II in 1979.

[1] Kung was secretly named a Cardinal in pectore in the consistory of 1979 by Pope John Paul II.

His funeral was held at St. John the Evangelist Church (now the Basilica of Saint John the Evangelist) in Stamford with Cardinal James Francis Stafford, President of the Pontifical Council for the Laity, presiding.

Kung's body was then transported to Star of the Sea Church in San Francisco, California, for a Low Mass with Cardinal Paul Shan Kuo-hsi of Taiwan presiding.

A requiem Pontifical High Mass using the Tridentine Liturgy in Latin was said the following day at Five Wounds Parish in San Jose, California, with Cardinal Shan again presiding.