Preventing Election Subversion Act of 2023 This bill prohibits the removal or suspension of local election administrators except for specified reasons and sets forth additional requirements for federal elections. Specifically, the bill restricts the ability of a statewide election administrator to remove a local election administrator. A statewide election administrator may suspend, remove, or relieve the duties of a local election administrator only for inefficiency, neglect of duty, or malfeasance while in office. Further, the bill directs statewide election administrators to report any removals or suspensions of local election administrators to the Department of Justice. The bill also establishes certain requirements for challenging an individual's eligibility to register to vote or vote in federal elections. In particular, the bill prohibits any person (other than an election official) from challenging an individual's voting eligibility unless the challenge is supported by personal knowledge.