Within a story there are two basic types of characters. If you’ve ever taken an English or a Literature class you already know these are called static and dynamic. Dynamic characters are those which undergo a dramatic change in their perspective or personality. Static characters remain the same without changing their ideals or personality.
In writing, this might seem like static characters don’t have an arc. This isn’t true. Static characters should have an arc, but it should end where they started. Their goals and motivation remain relatively unchanged. When writing a static character, completion of short-term goals shouldn’t affect who they are or how they view the world.
By contrast, dynamic characters will end their arcs in a different place than where they started. Their goals should be changed by the end of the story, as should their view of the world. The trials they face to complete their goals will challenge them and force them to grow in new ways.
Although it’s tempting to think of static characters as ‘bad’ characters, this isn’t true at all. Sherlock Holmes is a classic example of a static character who fills in the protagonist role quite well. More classics involved Cinderella, Gandalf the Grey and plenty of other characters both main and minor. Static characters are simply characters that don’t change. This may be because the trials they face don’t force them to change and can be solved with the perspective they already have. It may also be because the focus of the story isn’t on the character, but rather on the plot itself.
Dynamic characters can also be villains. the Dragon from Shrek is one such example, as is Hans from Frozen. Their original goal is changed through the events of the plot.