Although virtualization technologies have recently gained a lot of interest in Grid computing as they allow flexible resource management, the most common way to exploit grids still relies on dedicated services like resource management systems (RMSs) to get resources at a particular time. To improve resource usage, most of these systems provide a best-effort mode where lowest priority jobs can be executed when resources are idle. This particular mode does not provide any guarantee of service and jobs may be killed at any time by the RMS when the nodes they use are subject to higher priority reservations. This behaviour potentially leads to a huge waste of computation time or at least requires users to deal with checkpoints of their best-effort jobs. In this paper, we present Saline, a generic and non-intrusive framework to manage best-effort jobs at grid level through virtual machines (VMs) usage. We discuss the main challenges concerning the design of such a grid system, focusing on VM snapshot management and network configuration. Results of preliminary experiments show the interest of our proposal to ensure an efficient execution of best-effort jobs through the whole grid.