Which element of a literary adaptation should remain the same as the original work

Theme

Explanation:

Changing the theme of a story or Play changes the meaning of the piece

taking into account that a theme is the central topic a text treats and can be developed through a story, play, poem etc. the following are themes that can be further developed:  

my best friend jeffrey has many unusual interests. (the story could be about each of the unususal interests)

once a man gives his soul over to evil, he can never go back. (this could be a saying or a proverb)

the three sheepdogs lay around the yard all day. (it could be developed detailing how each of these sheepdogs lay around)

a priest's collar has an unusual effect upon people. (it could be developed detailing the different effect upon people)

innocence is a powerful force in a world full of corruption. (it could be developed detailing how is a world full of corruption)

king lear is a play shakespeare wrote later. (it is just a sentence and doesnt give any idea or topic to be discussed in details.

evil often wears the disguise of innocence. (this could be a saying or a proverb)