We consider a shared store based on distributed shared memory (DSM), supporting persistence by reachability (PBR). This is the simplest model for the distributed sharing of data. It is also the least constrained. A garbage collector writes reachable objects to disk, and reduces store fragmentation. Within a general model for DSM+PBR, we specify a distributed GC algorithm that is efficient and scalable. Its main features are: (i) it collects memory subsets independently from each other, even when replicated, (ii) it is orthogonal to coherence, (iii) it is asynchronous, and (iv) it provides a simple heuristic to collect garbage cycles, avoiding extra I/O costs. We describe the model, the current system, some performance results, and planned future work.