This paper examines care networks that operate on the blurred lines between religion and politics, civil society and the state, and everyday volunteerism and collective action. It argues that prevailing frameworks around "the poor" and "resistance" are insufficient for capturing the nuances of activism and care. This perspective often misses ways in which seemingly passive everyday volunteerism has the potential to transform the state's governmentality by weaving religious logic- welcoming the stranger, feeding the hungry, caring for the orphan, protecting human dignity- into the very "fabric of society, into norms, rules, institutions, and relations of power" (Bayat 2013, 25). Bayat's (2013) concept of "social nonmovements" offers a lens for analyzing how long-term, every-day care practices can quietly reshape or subvert state governance. Even if the state attempts to offset their subversive practices by submerging them in the state's logic of power, a social nonmovement can achieve notable reform and diminish the state's ability to neutralize their effects if the nonmovement continue to practice its "incremental disposition of claim making" (Bayat 2013, 25). This paper draws on qualitative data collected from 2023-2025 at humanitarian service sites and with local law enforcement to examine the refugee-migrant care network of the Rio Grande Valley. It argues that this network is participating in both "quiet encroachment" and "art of presence" (Bayat 2013) that may in fact be catalyzing significant social change. Specifically, this paper engages Bayat's social nonmovement framework to explore three questions: 1) What are the limitations of dominant perspectives on "the poor" and "resistance"? 2) What is social nonmovement? 3) How is this framework helpful for understanding the role and development of refugee-migrant care practices at border zones?