@Gilette Honestly? No. Unless it means whapping them across the face with them, old school duel-style.
That saying about how 'what you reward is what you encourage' applies here, too; coddling this behavior encourages it and makes it seem acceptable when it simply isn't so.
Provided there are options to negotiate, various opt-outs someone can take, limitations that can be agreed upon, etc., these folks are not in the position of 'innocent bystander with a gun suddenly at their head before the trigger is pulled, cope!'
The folks who can never lose, never look 'bad', never let someone else have the spotlight/etc. generally need a reminder that the game (in my case anyway, and in most others I have seen this is equally so) is intended for adults, and they'll be expected to behave like one even when things aren't going their favored way•. This is where things get into the territory others have mentioned re: 'won't accept anything bad happening to them ever/won't make sure they outshine everyone else in the scene at all costs' types, and they're typically pretty toxic to the game's ecosystem.
Being extra gentle with them really isn't the answer. Reminding them about the old playground rule about sharing all the toys is pretty essential, and this is more than most staff are ever willing to undertake. It's rare someone will speak up to say: "Hey, we've had repeated complaints about spotlight-hogging/unwillingness to take even a minor hit/etc." to this type, and generally ignore them in the vain hope that they'll shape up on their own.
There are fairly freeform, full-consent games where people can generally do this with impunity, and it's generally not a problem. Otherwise? Yeah, it's a problem, and it's not gonna fix itself. You can delicately mention it all you want, and generally it's not going to make an enormous difference if we're talking about one of the soap bubble ego types -- if they can't take a hit, they're generally going to be even less open to OOC criticism of any kind, no matter how constructive or kindly in its delivery.
• Most of what we need to know to play nice with others we really did learn as kids on the playground. (I have a whole theory about this just waiting to get flung at some poor, unsuspecting wiki somewhere, some day.) That said, as adults, maybe we've strayed too far from those days to remember those lessons, no matter how critical they tend to be to getting along in daily life. Share the toys. Toss the ball to other people, too! Don't throw a tantrum when the ball was thrown to somebody else; you'll get a turn, too! Share your snacks. Don't crack dirty jokes in front of the nuns. Staff needs nap time, too. If you get hurt, it's OK to cry and ask for help from the nurse, and it's not cool to laugh at somebody who's crying because they've been hurt. Don't break somebody else's toy just because you can when they've shared it with you.
The list goes on and on, but really, imagine how many problems would be averted if folks kept what we all learned as little kids in mind, you know?