How can I make a tool stay in someone's inventory after they die?

Put a folder in server storage and call it ToolsFolder any tools you want to save duplicate them and put them inside the folder then inside server script service put in a script and type this:

local dss = game:GetService("DataStoreService")
local toolsDS = dss:GetDataStore("ToolsData")

local toolsFolder = game.ServerStorage.ToolsFolder

game.Players.PlayerAdded:Connect(function(plr)

    local toolsSaved = toolsDS:GetAsync(plr.UserId .. "-tools") or {}

    for i, toolSaved in pairs(toolsSaved) do

        if toolsFolder:FindFirstChild(toolSaved) then 

            toolsFolder[toolSaved]:Clone().Parent = plr.Backpack
            toolsFolder[toolSaved]:Clone().Parent = plr.StarterGear 
        end
    end

    plr.CharacterRemoving:Connect(function(char)

        char.Humanoid:UnequipTools()
    end)
end)


game.Players.PlayerRemoving:Connect(function(plr)

    local toolsOwned = {}

    for i, toolInBackpack in pairs(plr.Backpack:GetChildren()) do

        table.insert(toolsOwned, toolInBackpack.Name)
    end

    local success, errormsg = pcall(function()

        toolsDS:SetAsync(plr.UserId .. "-tools", toolsOwned)
    end)
    if errormsg then warn(errormsg) end
end)

Put the gun in starter gear not in player backpack