Server Script in Workspace:

game.Players.PlayerAdded:connect(function(plr)
	local value = Instance.new("StringValue")
	value.Value = plr.Name
	value.Parent = game.Lighting.PlayerStore
	script.Trigger:FireAllClients(plr)
end)

game.Players.PlayerRemoving:connect(function(plr)
	if game.Lighting.PlayerStore:FindFirstChild(plr.Name) then
		game.Lighting.PlayerStore[plr.Name]:Remove()
	end
	script.Trigger2:FireAllClients(plr)
end)

LocalScript in StarterGui under a ScreenGui

local localplayer = game.Players.LocalPlayer
local currentSlot = 0
local back = script.Parent.Back
local players = game.Lighting.PlayerStore:GetChildren()

local function updatelist()
	for i,v in pairs(back:GetChildren()) do
		v.Position = UDim2.new(.02, 0, 0, (35*currentSlot))
	end
	back.Size = UDim2.new(.2, 0, (.048 * currentSlot), 0)
end

game.Workspace.Script.Trigger.OnClientEvent:connect(function(plr)
	local player = plr.Name

	if player ~= localplayer.Name then
		local default = script:WaitForChild("Default"):Clone()
		default.Parent = back
		default.PlayerName.Text = player
		default.Name = player
		default.Slot.Value = currentSlot
		default.Position = default.Position + UDim2.new(0, 0, 0, (35 * currentSlot))
		back.Size = back.Size + UDim2.new(0, 0, (.048 * currentSlot), 0)
		currentSlot = currentSlot + 1
	elseif player == localplayer.Name then
		for i,v in pairs(players) do
			local default = script:WaitForChild("Default"):Clone()
			default.Parent = back
			default.PlayerName.Text = v.Value
			default.Name = v.Value
			default.Slot.Value = currentSlot
			default.Position = default.Position + UDim2.new(0, 0, 0, (35 * currentSlot))
			back.Size = back.Size + UDim2.new(0, 0, (.048 * currentSlot), 0)
			currentSlot = currentSlot + 1
		end		
	end
end)

game.Workspace.Script.Trigger2.OnClientEvent:connect(function(plr)
	local player = plr.Name --Here it errors, it says plr is nil?
	local slot
	for i,v in pairs(back:GetChildren()) do
		if v.Name == player then
			slot = v.Slot.Value
			v:Destroy()
		end
	end
	if slot ~= nil then
		for i,v in pairs(back:GetChildren()) do
			if v.Slot.Value > slot then
				v.Slot.Value = v.Slot.Value - 1
			end
		end
	end
	currentSlot = currentSlot - 1
	slot = nil
	updatelist()
end)

I am making a custom PlayerList, and for some reason, it returns player as nil (I put a note next to where it is erroring at)

Help is appreciated, thanks! :D

Replication

It's nil because it genuinely is nil. Because the player was removed from the game, aside from the closure of the Instance, it is no longer replicated and does not exist on the client. Solution? Connect to the events locally - It works now.

In the off chance that it doesn't work locally, send the UserId instead.