Must We Send a Correction If a Student's Pell Eligibility Does Not Change After a Non-Verification Correction?

It depends. For a student who is not selected for verification, either the school or the student must correct any errors on the original FAFSA and submit those corrections to the FAFSA Processing System (FPS) for reprocessing, but only if those corrections would change the student's student aid index (SAI) or be used to determine the student's eligibility for Title IV aid. 

Of course, if you have conflicting information you will need to resolve it, regardless of whether or not the application was selected for verification by ED. To ensure the accuracy of the application, a correction will need to be sent to the FPS for processing [See 34 CFR  668.16(f)]. 

NASFAA's Compiled Title IV Regulations may be found under Tools & Resources on the NASFAA website.

Student Aid Reference Desk: For additional information, try the Student Aid Reference Desk. It is a central hub of all the important financial aid resources you need with direct links to legislation, regulation, Dear Colleague Letters, and other ED and NASFAA references. It is updated on a rolling basis with the latest news and changes.