The study addresses the challenges faced by members of support networks for older adults hospitalized in palliative care, based on the research question: who comprises these networks, and how do they balance caregiving demands with the demands of the labor market? To answer this question, a qualitative, descriptive, and field-based approach was adopted. Data collection took place in a large hospital in the state of Rio Grande do Sul, involving two groups: 15 older adults hospitalized in palliative care and 18 members of their support networks, indicated by the older adults themselves. Data were collected in two stages: (i) application of the network map instrument with the hospitalized older adults and (ii) semi-structured interviews with members of their support networks. Data analysis followed the content analysis technique, with emerging categories organized based on participants' narratives. The emerging categories were: a) who comprises the support network: familism and the feminization of care; b) vulnerability of the support network: income, work, and mental health at risk; c) between work and the hospital: challenges of being present. The results highlight that support networks are scarce and limited to the family sphere, with no significant backing from public services. The study also reveals the overburdening of women in caregiving roles, reinforcing the familist logic of Brazilian social protection. It was found that there is a precarious balance between work and caregiving responsibilities, leading to increased caregiver vulnerability, financial strain, and negative impacts on mental health. The study concludes that family members, especially women, find themselves walking a tightrope between the demands of hospital care, domestic caregiving, and the labor market. The study reinforces the urgent need for public policies that ensure dignified caregiving conditions.