I have seen this in games like Miners Haven. It shows a gui before the server shutsdown. Same thing happens when your about to shutdown a game with hd admin. What I would like to know is how you can use a script to see when this is about to happen.
Hello sir you can Detect if the server is shutting down using BindToClose function (https://developer.roblox.com/api-reference/function/DataModel/BindToClose) There are scripts called soft shutdown you can search it in roblox studio they are a great demonstration of how it works. Also sry for bad english.