The claim describes advice given by a top adviser regarding the prudent use of a proposed accountability system to maintain civil servant morale. While the evidence confirms discussions around an accountability system and policy addresses, none of the provided web search results or Wikipedia entries contain the specific advice attributed to 'a top adviser to the city's leader' regarding morale preservation. The evidence is insufficient to corroborate this specific advisory statement across multiple independent sources.

The claim attributes specific statements to 'Ip, formerly the city’s director of immigration' regarding investigations considering departmental responses and efficiency improvements. The provided evidence for this claim consists only of general web search results related to immigration enforcement (U.S. context) and does not contain any mention of 'Ip' or the specific policy advice mentioned in the claim. Therefore, corroboration is impossible with the given evidence.

The claim details the specific criteria (widespread, repetitive and systemic, or personal implication) and the initiating parties (city leader, department secretaries, or bureau directors) for investigations by the Public Service Commission. While the evidence confirms the existence of a proposed mechanism and the role of the Public Service Commission (via web search context), the precise details regarding who can initiate investigations and the exact criteria ('widespread, repetitive and systemic') are not independently corroborated by multiple sources. The evidence suggests this is a specific detail from the primary reporting context.