Blog owners would happily rename posts - and see a new URL, with no problem. Those blog owners who monitored search engine activity, however, later became concerned by the "404"s, shown in the search engine activity logs, in Webmaster Tools - or from various test searches.
Blogger later gave us dashboard and post editor options, to let us intentionally change a post URL, when necessary - and stopped allowing incidental changes to the date or URL, when editing post content.
Settings - Search preferences has the "Custom Page Not Found" and "Custom Redirects" wizards, for dealing with existing posts with changed URLs - and the Post Editor "Post settings" has the "Permalink" wizard, to change URLs of new posts.
This gives blog owners the ability to Edit and Publish posts, and to adjust URLs, independently - and makes it harder for owners to accidentally generate "404"s with existing posts.
You can change a post to Draft status, to change the date or URL.
Recently, people discovered that changing a Published post, to Draft status, would reset a post. A Published post, changed to Draft, and later Published again, would act as a new post would have, when Published.
Blog owners wishing to change the URL of an existing post would change a post back to Draft status, change the Date and / or Title, then Republish - and the post would have a new URL to match the new Date / Title.
This worked great - for owners intentionally wanting a new URL for their renamed posts.
You can also publish a post to Draft, to re use the URL of that post.
If you delete a post, then publish a new post with that same title, you will get a post with a URL containing a duplication prevention suffix - because deletion of a post does not let you re use a URL. If you publish a post to Draft, that resets the URL - and lets you publish a new post to that same URL.
Saving a post as Draft, to edit, can allow URL change - and cause broken links.
Some blog owners use Draft status, for previously Published posts, differently
You can take a published post offline, as a Draft post - then change the Title, and various other settings. This will not change the URL - unless you also change the Permalink, before you Publish.
If you do change the URL, be mindful of the links that may refer to the old URL.
If you want the URL to change, you will have to change the permalink.
While the post is in Draft status, find "Permalink" in "Post settings", in the right sidebar of post editor. Select "Custom Permalink", and change the title section of the post URL. Then select "Done".
Note you will only be able to change the title section of the permalink. You can't change the year, month, or extension ("html") any more.
If I wanted to, I could rename this post, when in Draft status.
Change Posts To Draft, To Change The Post URLs
I could change the post URL, to match.
The most obvious change that I could get, then would be
Fix broken links, by adding a custom redirect.
We can use the same tools to correct mistakes, as we can to make changes.
If you change the URL - and cause broken links, and / or "404" entries in Search Console / Webmaster Tools, when re Publishing a Draft post, just add a Custom redirect from the old URL, to the new URL. One new redirect takes but a few seconds to add - and will keep your readers, the search engines, and you happier.