When you close your trading terminal application with any open orders, those orders remain active even if the application is closed. You must manually close any orders before exiting your trading terminal application or they will remain active.
However, when a Stop Out occurs while you are not logged in, orders can be closed without your trading terminal being active.
Another scenario to consider is Expert Advisors (EAs) and scripts, if installed, can also close orders automatically while you are offline if they are set to run while connected with a Virtual Private Server (VPS).