Any idea how to remove players from table?

So its a hunger games kinda like script. It has a working District system etc. its very simple for now.

I have a 10 second round time for testing purposes and i know how to check how many Players are left in the table.

How would i make "leave/Death" Script which removes the Players who leaves/dies from the table? Its kinda hard to understand this script ( atleast it was for me until now) but i would appreacite if somebody could help me out <3

I tried to do an Leave/Death script but its not working out.. here:

--Side Note, i dont even know if i use the correct Variables like _G.Districts (Also this is in a diffrent script). 

game:GetService("Players").PlayerAdded:Connect(function(player)	-- Death Script
	player.CharacterAdded:Connect(function(character)
		character:WaitForChild("Humanoid").Died:Connect(function()
		local Update = {}
		for i, v in pairs(_G.Districts) do
		    if v ~= player.Name then
			   table.insert(Update,1,v)
		    end
		end
	_G.Districts = Update
		end)
	end)
end)

game:GetService("Players").PlayerRemoving:Connect(function(player)	--Leave Script

	local Update = {}
	for i, v in pairs(_G.Districts) do
		if v ~= player.Name then
			table.insert(Update,1,v)
		end
		
	end
	_G.Districts = Update
end)

Here is the Main Script

--//Services
local Players = game:GetService("Players")
local ReplicatedStorage = game:GetService("ReplicatedStorage")

--//Remotes
local Remotes = ReplicatedStorage:WaitForChild("Remotes")
	local Names = Remotes:WaitForChild("Names")
	local Round = Remotes:WaitForChild("Round")
	
--//Variables 
local Tributspawn = workspace:WaitForChild("Tribut")

--//Functions
	function Shuffle(Table)			--This function is for some math stuff regarding the District System
    local Size = (#Table)
    for i = Size, 1, -1 do
        local RandomObject = Random.new():NextInteger(1, Size)
        Table[i], Table[RandomObject] = Table[RandomObject], Table[i]
   		end
    return Table
end	
	
--//Main
while true do
	wait(3)
	_G.Districts = {}		
local Players = (Shuffle(game:GetService("Players"):GetPlayers()))
 
for i = (1),(math.ceil(#Players/2)) do
    _G.Districts[#_G.Districts + 1] = {}
end

for Player = (1),(#Players) do
    local DesiredDistrict = (math.ceil(Player/2))
    table.insert(_G.Districts[DesiredDistrict], Players[Player])
Names:FireAllClients(DesiredDistrict,Players[Player])		--This is for a Gui which pops up and shows the Playername , Playerdistrict and the Character Image (ignore it)
wait(2)
end
	print("Round starts")
		for t = 10,0,-1 do
		wait(1)
			print(t)
			print(#Players) --To see how many Players are in the round
			if #Players == 0 then 	--Still has no point to be here until there is no working death/leave script. But if the script is there its then there to check if it works
			print("Everybody died")
			break
		end
	end
end