I remember being surprised as a student when I learned that a solid body, rotating on other than its principal axis, could suddenly shift to start rotating about another axis. It turns our that this phenomenon can occur even with planets, and when it happens, it is called True Polar Wander, or TPW.
It turns out the Earth has experienced a few of these events, where the axis of rotation changes by sixty degrees or so. As you might expect, these tend to be rather catastrophic events. Imagine, say, New York winding up at the North Pole. Typically these result in mass extinctions.
So what could produce such a thing? Perhaps a major volcanic eruptive event or mountain building episode might place a major mass in an unbalanced position with respect to the axis.