Automations save in two stages, so a half finished edit can never reach people who are part way through a flow.
While you work:
Your changes are saved automatically every few seconds as a draft. The draft is not live. Anybody already moving through the automation keeps following the published version.
When you press Save automation:
The draft is published and becomes the live flow.
If you close the tab and come back, you are shown your unsaved work with a notice at the top saying it is not live yet. From there you can either press Save automation to publish it, or press Discard draft to throw the changes away and go back to the published version.
This means you can safely edit a running automation, take as long as you like, and nothing changes for your subscribers until you decide it should.