The contradictions between food poverty affecting a large section of the global population and the everyday wastage of food, particularly in high income countries, have raised significant academic and public attention. All actors in the food chain have a role to play in food waste prevention and reduction, including farmers, food manufacturers and processors, caterers and retailers and ultimately consumers. Food surplus redistribution is considered by many as a "win-win" solution for food waste reduction and food poverty mitigation, while others criticize charitable initiatives as inadequate responses, that inhibit governments from responsibly protecting the citizens right to food. This paper frames food assistance as "hybrid systems", situating at the intersection of territorial food, public welfare and third sector voluntary systems. Based on available literature and reflections from previous research examining the discourse surrounding food banks in Italy, we develop a system dynamics conceptual mapping. The aim is to model a set of relations and dynamic mechanisms associated with variables relevant to food waste generation, food recovery for social purposes and food poverty alleviation. The analysis of feedback interactions highlights the (actual and potential) vulnerabilities of food assistance systems that occur when addressing food poverty by reducing food surplus. In summary, as the awareness on food poverty and food surplus rises, incentives to food recovery and redistribution strengthen the role of (voluntary) food assistance actors, increasing their exposure to drivers of change, such as retailers' standards for food surplus prevention. This paper contributes to the current academic debate on charitable food assistance, with insights for policy makers and other system actors.