You can close down csgosl and keep the server running. When you later start csgosl it will adjust to the current server status.
If you host a buggy workshop map which causes the server or connecting clients to crash remove the map folder from /server/csgo/maps/workshop/ and restart csgosl.
If server installation or update fails make sure your disk is not full. A full disk will cause weird error messages during updates (steamcmd will not indicate a full disk but instead just give an error code).
The command line used to start the server is always traced (on linux to the terminal window and on windows under the console tab). This command line can be used to start the server manually e.g. when playing around with different settings in the configuration files.