Sigil automatically runs an HTML tidy process on save (and in a couple of other situations) that ensures that it never saves malformed HTML to disk. Cleaning up stray closing tags is a pretty safe thing for it to do.
I also frequently take advantage of it to add closing tags as well. For example, I sometimes do a search and replace to turn "<p>Chapter" into "<h2>Chapter", and then the tidy step turns the corresponding </p> tags into </h2> tags. A quick and dirty way to format chapter headers, though it's important to manually check to make sure it generates a nice table of contents to catch any glitches.