What is wrong with this script? [Unanswered]

It's supposed to check every tenth of a second to see if the 'owner' has left the game, and if he/she has then reset the tycoon.

while true do
wait(0.1)
game.Players.PlayerRemoving:connect(function(player)
    if player.Name==script.Parent.Owner.Value then 
    script.Parent.Owner.Value = "Nobody" 
    ------------------------------------
    local gate = script.Parent.Gate
    if gate.Transparency ~= 0 then
        gate.Transparency = 0
        gate.CanCollide = true
    end
    ------------------------------------
    local co = script.Parent.OwnershipDoor.ClaimOwnership
    co.BrickColor = BrickColor.new("Medium stone grey")
    co.Parent.OwnerName.SurfaceGui.Owner.Text = "Claim Ownership"
    co.Defender.Disabled = true
    co.Claim.Disabled = false
    ------------------------------------
end end)
end

You don't need to run a while loop for a function. A function is called upon what you said... in this case, when a player leaves.

Look at it like this, I join a game, finish my tycoon and decide to leave. Your code looks as follows:

game.Players.PlayerAdded:connect(function(player)
	-- code here
end)

So, I hit the X in the corner of the screen. All of your code inside of that first function is run, and I am now known as 'player'. So now you can see if me (player) has reset my tycoon and any other stuff.

Side Note

Instead of doing a seperate wait() inside of a while loop, you can write the code as while wait() do.

For all of those BrickColor.new("Medium stone grey")'s you can easily do BrickColor.Gray(). To check if the color will work for you (.Gray() does Medium stone grey), you can run this in the command line: print(BrickColor.Gray()). Use this Wiki page to learn more about BrickColors.

Anything else, let me know!

If it's a LocalScript, then PlayerAdded and PlayerRemoving doesn't work. Instead, use ChildAdded and ChildRemoved.

game.Players.ChildRemoved:connect(function(child)
	if child.ClassName == 'Player' then
		--Code goes here
	end
end)

Here's using the above in your script:

while true do
	wait(0.1)
	game.Players.ChildRemoved:connect(function(child)
		if child.ClassName == 'Player' then
			local player = child
			if player.Name==script.Parent.Owner.Value then 
				script.Parent.Owner.Value = "Nobody" 
				------------------------------------
				local gate = script.Parent.Gate
				if gate.Transparency ~= 0 then
					gate.Transparency = 0
			        	gate.CanCollide = true
			    	end
				------------------------------------
				local co = script.Parent.OwnershipDoor.ClaimOwnership
				co.BrickColor = BrickColor.new("Medium stone grey")
				co.Parent.OwnerName.SurfaceGui.Owner.Text = "Claim Ownership"
				co.Defender.Disabled = true
				co.Claim.Disabled = false
				------------------------------------
			end
		end
	end)
end