The Avignon Papacy and the Western Schism (1309-1417), when the papacy moved to France and later split into competing popes.
The engine treats this as a stress-test that the Church's institutional backbone passed.
The papacy sat in Avignon under French influence from 1309 to 1377, then the Western Schism (1378-1417) produced two or three rival popes at once. Even so, the underlying legal and financial system kept running through decades of divided leadership.
It proves the Church's real strength wasn't a single leader but the durable legal and financial apparatus that survived even open schism.