How can I make it so when a there is only one player alive the loop breaks?

you can't have two while loops running simultaneously. one loop should be enough to do the job.

EDIT: fixed player checking

local text = game:GetService('ReplicatedStorage'):WaitForChild('TextValue')
local Players = game:GetService('Players')
local PlayersLeft

local IsPlayingFolder = Instance.new('Folder')
IsPlayingFolder.Parent = game:GetService('ServerStorage')

function DoubleCheck()
    local pl = #Players:GetChildren()
    if pl <= 1 then
        return true
    else
        return false
    end
end

workspace.BackGroundMusic:Play()
while wait(1) do
    PlayersLeft = #Players:GetChildren()
    if PlayersLeft <= 1 then
        text.Value = "Not enough players..."
        print("Not enough players")
    elseif PlayersLeft > 1 then
        text.Value = "Intermission"
        print("Intermission")

        wait(15)

        if DoubleCheck(PlayersLeft) == true then
            text.Value = "Not enough players..."
            --double check if everyone's there
            return
        end

        text.Value = "Game is starting"
        print("Game is starting")

        wait(5)

        for i,v in pairs(Players:GetChildren()) do
            local newValue = Instance.new("BoolValue")
            --value type doesn't matter, just the name
            newValue.Name = v.Name
            newValue.Parent = IsPlayingFolder
        end

        local plrplaying = IsPlayingFolder:GetChildren()
        for i,v in pairs(plrplaying) do
            local num = math.random(1,8)
            local plr = Players:FindFirstChild(v.Name)
            if plr and plr.Character and plr.Character:FindFirstChild("Head") then
               plr.Character.Head.CFrame = CFrame.new(workspace.Teleports["Part"..num].Position)
            end
        end

        text.Value = "Welcome to Chances of Doom..."
        wait(5)
        text.Value = "Let's begin."
        wait(5)
        text.Value = "A random player will be eliminated..."
        print("a rando will be elim")
        wait(10)
        workspace.Lightbulb.Lightbulb.Light.Color = Color3.new(170,0,0)

        PlayersLeft = Players:GetChildren()
        print("Players left: "..#PlayersLeft)
        if #PlayersLeft > 1 then
            local eliminated = PlayersLeft[math.random(1,#PlayersLeft)]
            if eliminated.Character and eliminated.Character:FindFirstChild('Humanoid') then
                eliminated.Character.Humanoid.Health = 0
            end
            if IsPlayingFolder:FindFirstChild(eliminated.Name) then
                IsPlayingFolder[eliminated.Name]:Destroy()
                --removes their in game presence after killing
            end
            wait(3)
            text.Value = eliminated.Name.." has been eliminated."
            wait(5)
        elseif #PlayersLeft == 1 then
            print('Only one person in-game!')
            return
        end

        workspace.LightBulb.Lightbulb.Light.Color = Color3.new(255, 255, 255)
        wait(5)
        text.Value = "Anyway, let's move on..."
        wait(5)
        local PlayersLeftPlaying = IsPlayingFolder:GetChildren()
        if #PlayersLeftPlaying == 1 then
            text.Value = PlayersLeftPlaying[1].Name.." is the last man standing! Restarting..."
            wait(5)
            for i,v in pairs(IsPlayingFolder:GetChildren()) do
                v:Destroy()
                --make sure no values are left
            end
            return
        end
        --moving on?
    end
end