The emerging field of passive macro-scale tilebased self-assembly (TBSA) holds promise for enabling effective manufacturing processes by harnessing TBSA's intrinsic parallelism. However, the current TBSA methodology still does not fulfill its potential, largely because such assemblies are typically error-prone and the size of an individual assembly is limited by a lack of mechanical stability. Moreover, the instability issue becomes worse as assemblies become larger. Here, using a novel type of tile that is carried by a bristle-bot drive, we propose a framework that reverts this tendency; i.e., as an assembly grows, it becomes more stable. Using physicsbased computational experiments, we show that a system of such tiles indeed possesses self-stabilizing characteristics and enables building assemblies containing hundreds of tiles. These results indicate that one of the main current limitations of mechanical, agitation-based TBSA approaches might be overcome by employing a swarm of free-running sensorless mobile robots, herein represented by passive tiles at the macroscopic scale.