Bart: Yeah!
Principal Skinner: And Lisa, you have a choice. You may continue to be challenged in third grade, or return to second grade and be merely a big fish in a little pond.
Lisa: Big fish! Big fish!
Change isn't always a good thing, nor necessary. Likewise some characters, be they rounded or flat, will end a story with pretty much the same personality and traits they began with. These Static Characters can go entire seasons or books without changing or experiencing the Character Development that a more Dynamic Character does. If they ever learn a lesson that might make them change noticeably, they will always immediately forget all about it by the next episode. Learned nothing and forgotten nothing, if you will.
This isn't necessarily a bad thing, as some characters don't NEED Character Development. A badass for example does not have to decay into The Woobie to stay an interesting character. While some consumers may embrace the evolution, others will cry out, "We Want Our Jerk Back!" Such characters are useful in secondary roles, serving as yardsticks against which your central (and dynamic) character's growth can be a foil. If you want your Static Character in the central role, just enforce it internally, using a Pygmalion Snapback or a painful collision with Status Quo Is God. Some comedies are built around characters whose personalities are set in stone and will never change, whatever happens. For that matter, every tragedy is built around characters whose personalities are set in stone and will not change, whatever happens.
Also note that Static Characters are not by definition boring. Obviously, it helps if you've got a Round Character, as exploring all their pre-existing facets can entertain without requiring character evolution. Furthermore, the introduction of Hidden Depths or an exploration of a Dark and Troubled Past accomplishes similar things; while the character is technically not evolving, the audience's perception of the character very much does. And these characters are ripe for internal conflict, since we already know a fair bit about them. Interest can also be wrung out of exploring how and why the character stays so constant in the face of the dramatic events of the plot — this can in itself be evidence of unusual self-assurance, determination or unflappability.
Having said that, Flat Characters who are also Static may begin to get dull unless the author takes care to make them entertaining somehow, be they the Butt-Monkey or perpetual Fish out of Water.
Despite their unchanging nature, a different personality during Early-Installment Weirdness can still be a distinct possibility; Static Characters are frequently the result of Flanderization.
Static Characters are not to be confused with the superhero Static.
