This study aims to clarify the concept of budget resilience and substantiate an approach for selecting indicators of regional budget resilience. A content analysis of scientific sources in the field of budget resilience was conducted, and current approaches to defining the concept of budget resilience were classified. The author’s interpretation of the concept is presented, emphasizing the need to select indicators that assess regional budget resilience by considering the interests of public funding recipients. Within this framework, groups of recipients—regional authorities, economic entities, and the population—are identified, and their interests are determined. A system of indicators is proposed to ensure budget resilience in the region, reflecting the level of interest satisfaction among these groups. A comparative analysis of the balance of recipients’ interests based on the results of budget policy and the budget process in the Russian Arctic regions was carried out, and trends in their economic interactions under conditions of global instability were analyzed. The study found vulnerabilities in the budget resilience system, manifested in the infringement of recipients’ interests. Changes in financial market conditions and resource prices led to a decrease in financial results for companies and a reduction in regional output redistributed through budgets, resulting in welfare loss for the regions and their populations. To address the situation, it is necessary to intensify investment activities and business development in the regions and optimize the fiscal regulation system, which will ultimately contribute to the growth of budget and household incomes. Changes in these indicators should be monitored not only in national currency but also in dollar terms to assess the recipients’ financial well-being on an international scale. Future research will focus on selecting specific indicators and their threshold values for assessing budget resilience in the Russian Arctic regions.