If there are any roles in the game that would cause an investigative role to return an incorrect result (Godfather, Miller, Ninja, etc.), those abilities will only function while you are alive.
After your death, all investigations will be guaranteed to return the correct result for their target.
You win if the game ends while you are alive, regardless of any other factors.
Living Falsification Enablers/Disablers will always take priority over dead Falsification Enablers/Disablers. If there are multiple conflicting Falsification Enablers/Disablers alive, Falsification Enablers will have priority. If there are no living Falsification Enablers/Disablers, only the most recently killed will take effect. For example, if a game has one Falsification Enabler, and one Falsification Disabler, all falsifying roles will function normally until the Falsification Enabler is killed. If the Falsification Disabler is killed afterwards, all falsifying roles will reactivate. If the Disabler is killed first, there will be no change unless the Enabler is later killed, at which point all falsifying roles will be deactivated.