We define the Repeat Offender Problem (ROP). Elsewhere, we have presented the first dynamic-sized, lock-free data structures that can free memory to any standard memory allocator—even after thread failures—without requiring special support from the operating system, the memory allocator, or the hardware. These results depend on a solution to the ROP problem. Here we present the first solution to the ROP problem and its correctness proof. Our solution is implementable in most modern shared memory multiprocessors.