Digital upskilling and remote work are frequently presented as pathways for displaced communities who face political, economic crises and employment barriers. The viability and stability of available energy infrastructures for these communities is critical to the long-term success of these proposed job trajectories. In this paper, we investigate how 17 Syrian refugees living in Lebanon navigate their local unstable energy infrastructures to conduct digital gig work and receive digital training. We found that digital gig work and training are workarounds to the political and social inaccessibility of local labor markets for refugees and that participants rely on a series of material energy strategies to optimize their electricity access. We argue that to support refugees conducting digital gig work and training, we must recognize and account for ecological, social, and technological limitations and frailties in the development of technological solutions and draw our attention to how infrastructures are perpetually undergoing processes of breakdown, repair, and renewal. We argue that this attention to ongoing transformation and renewal creates new opportunities for productive and creative reconfiguration as well as modes through which CSCW may intervene in unstable energy contexts. From this perspective, we emphasize the importance of better resourcing displaced communities with information regarding energy access and supporting them in establishing and strengthening their own visions for alternative energy systems and employment pathways.