Why does my animation still play even though I unequip a tool?

You want to create and use LoadAnimation outside of these events so both event functions has the animation.

Also you want to disconnect the running event so that you don't create it over and over again.

local plr = game.Players.LocalPlayer

local IdleAnim = script:WaitForChild("Idle")
local RunAnim = script:WaitForChild("Run")

local run = plr.Character.Humanoid:LoadAnimation(RunAnim)
local idle = plr.Character.Humanoid:LoadAnimation(IdleAnim)

local runE

script.Parent.Equipped:Connect(function()
    runE=plr.Character.Humanoid.Running:Connect(function(value)
        if value>0 then
            playrun()
        else
            playidle()
        end
    end)
end)


script.Parent.Unequipped:Connect(function()
    run:Stop()
    idle:Stop()
    if runE then
        runE:Disconnect()
        runE=nil
    end
end)


function playidle()
    run:Stop()
    idle:Play()
end

function playrun()
    idle:Stop()
    run:Play()
end

I can't tell you if it's the issue but i think that you need to use :Disconnect()

    local plr = game.Players.LocalPlayer
    local equiped = true
    IdleAnim = script:WaitForChild("Idle")
    RunAnim = script:WaitForChild("Run")
    local run = plr.Character.Humanoid:LoadAnimation(RunAnim)
    local idle = plr.Character.Humanoid:LoadAnimation(IdleAnim) 

    script.Parent.Equipped:Connect(function()
        equiped = true
        plr.Character.Humanoid.Running:Connect(function(value)
            if equiped == true then
            if value>0 then
                playrun()
            else 
                playidle()
            end
            end
        end)
    end)


    script.Parent.Unequipped:Connect(function()
        equiped = false
        run:Stop()
        idle:Stop()
    end)


    function playidle()    
        run:Stop()
        idle:Play()
    end

    function playrun()
        idle:Stop()
        run:Play()
    end

I think you need a Disconnect() in there