##Give them a reason to take risks
Death is, at the very least, an inconvenient setback, and often much more. So why shouldn't they be cautious?
That's not a rhetorical question - really think about your answer. So far, it hasn't caused a problem, so there's no reason to change. You're right, though, that it has potential drawbacks as the story goes further on. Maybe they'll hang back at a crucial moment and get other players killed. Maybe they'll refuse to bite at a story hook you really want them to grab. Or maybe they'll be forced to take a risk and resent it, making the game less fun.
So, what to do about it? Your question is about reassuring the player that it's okay to take risks, and some other answers are about demonstrating that paranoia is unnecessary. That may be part of your answer - but even if the risks are small, why take any you don't have to?
The answer is motivation. What does your player want out of this game? Cool new powers? To explore the psychodrama of being a rampaging warrior and balancing killer instincts with social pressure? Assuming your player is at least a little bit into the roleplaying part of RPGs, work with them to define what their character wants out of life. Magic items? Friendship? To conquer a kingdom? Make it clear that these things are all possible... if you can stomach a little risk.
It's worth noting that once you've done this, you shouldn't force it - when you put a reward behind a risk, weighing those and choosing how to react is a big part of being a player in an RPG.
But in general, the key is that both the player and the character have to want something. No one will jump over a puddle, let alone cross oceans, if there isn't something they want on the other side.
