Committed Hero
Hero
I'd agree with Umbran here. The player's don't have to go looking for danger, the danger will come looking for them whether they want it to or not. In fact, that makes it more frightening because despite the characters best intentions, where they thought they were safe, they were in fact not.
Horror is about survival first and foremost, and if that means killing/defeating the bad guy to do it (if possible) then so be it. Horror is one of the few genres left where PC's should be regular humans without any kind of extra powers. Maybe they might be some bad hombre ex-Spec Ops type, but against the horror that may barely be enough. To be frightening, mortality of the characters must be ever-present.
I think the GM and players need to be on the same page. If the former is expecting a X of Cthulhu game of investigation and risking horror to fight it, and the PCs run from their ability to do so, both sides will be dissatisfied.