The solution clearly can't be to never ever fix bugs though.

But depending on the kind of bugs (especially when they are of the "gotcha"/"UX" kind) often it's better to just create a new API version with the corrected behaviour and keep existing software apply handle the old behaviour the best they could.

But clearly for many many other kinds of bugs (security etc) we are better served with a bug fix in the old API even if that implies a possibility for breaking somebody.