What does the warden decide to do after Zero runs away in Holes?

After Zero runs away the Warden decides not to notify anyone. Because Zero is a ward of the state, and has no legal guardians, she assumes no one will come looking for him if he dies out in the desert. She orders that all of Zero's files be destroyed, as if he was "never here".

When a new boy, "Twitch" replaces Zero at Camp Green Lake, Stanley realizes is he doesn't go after Zero, no one will. This eventually leads to Stalney stealing Mister Sir's truck, crashing it, and having to go after Zero on foot.

What was the Warden's plan about Zero's disappearance in Holes?

In chapter 30, emotions come to a boiling point when Zigzag attacks Stanley and Zero gets involved. When the counselors arrive, Stanley admits that Zero has been digging his hole in exchange for reading lessons. The counselors proceed to embarrass Zero by quizzing him, and Zero suddenly announces that he is done digging holes. Zero then uses his shovel as a weapon and strikes Mr. Pendanski in the face before running off into the desert. The Warden instructs the counselors to not run after Zero and assures them that he will have to return for water.

In the next chapter, Stanley blames himself for Zero's disappearance and hopes that he can find God's Thumb. When Stanley returns to the tent, the Warden, Mr. Sir, and Mr. Pendanski ask him if he has seen Zero. Stanley then overhears them discussing their plan about covering up the entire situation. Mr. Pendanski informs the Warden that Zero is a ward of the state and does not have any family. Mr. Pendanski also tells the Warden that Zero does not have a social worker who took an interest in him and the Warden instructs Mr. Pendanski to delete all of Zero's records.

In addition to Zero's records, the Warden also instructs Mr. Pendanski to delete his state files. Essentially, the Warden's plan is to delete every record and file associated with Hector Zeroni to prevent the attorney general from investigating his disappearance.