Is there a way to make a StarterPack failsafe?

This is an infinite check (use if you have no other code to execute below this function and you want the player to have a sword at all times):

local function onTouched(human)
    local tool = game.ReplicatedStorage.LinkedSword
    local player = game.Players:FindFirstChild(human.Parent.Name)
    local h = human.Parent:FindFirstChildWhichIsA("Humanoid")
	while true do
	wait(2) --Change the number to how long (in seconds) you want to wait until it checks again.
    	if human.Parent:FindFirstChild("LinkedSword") then
       		print("This Player has a sword")
    	else
        	print("This Player has no sword")
        	tool:Clone().Parent = player.BackPack
		end
	end
end

script.Parent.Touched:Connect(onTouched)

Note: the above script was not edited in its' entirety. It was only edited by adding a "checking" system.

Otherwise, use a short-term check (only edited lines 6 through 15):

local function onTouched(human)
    local tool = game.ReplicatedStorage.LinkedSword
    local player = game.Players:FindFirstChild(human.Parent.Name)
    local h = human.Parent:FindFirstChildWhichIsA("Humanoid")
	local i = 0
	repeat
    	if human.Parent:FindFirstChild("LinkedSword") then
       		print("This Player has a sword")
    	else
        	print("This Player has no sword")
        	tool:Clone().Parent = player.BackPack
		end
		i = i+1
		wait(2) --Change the time to how long you want to wait until it checks again.
    until i == 3 --This script checks for the sword 3 times.
end

script.Parent.Touched:Connect(onTouched)

Note: the above script was not edited in its' entirety. It was only edited by adding a "checking" system.

Edited script for ServerScriptStorage:

function onPlayerAdded(plr)
	local tool = game.ReplicatedStorage.LinkedSword
	while true do
		wait(2)
		if plr.Backpack:FindFirstChild("LinkedSword") or workspace:FindFirstChild(plr.Name):FindFirstChild("LinkedSword") then
			print("This Player has a sword")
		else 
			print("This Player has no sword")
			tool:Clone().Parent = plr.Backpack
		end
	end
end

game.Players.PlayerAdded:Connect(onPlayerAdded)

Note: this script is fully edited and proofread in its' entirety.