Final answer:
Verification of eligibility for ESM or BAS is usually handled by the administrative or financial departments within the organization offering these benefits, such as a school's financial aid office or a military's personnel support department.
Step-by-step explanation:
The responsibility for verifying eligibility for ESM (Exceptional Student Meal) or BAS (Basic Allowance for Subsistence) typically falls on the administrative or financial department within the organization that administers these programs. In the context of educational institutions, this could be the financial aid office, or in the military, it might be the personnel support department. They ensure that applicants meet the necessary criteria, which could include factors such as income level, dependency status, and enrollment in a certain number of course units for ESM, or rank, dependency status, and duty status for BAS.