We study the question of whether the "termination with probability 1" property of a randomized algorithm is preserved when one replaces the atomic registers that the algorithm uses with linearizable (implementations of) registers. We show that in general this is not so: roughly speaking, every randomized algorithm A has a corresponding algorithm A' that solves the same problem if the registers that it uses are atomic or strongly-linearizable, but does not terminate if these registers are replaced with "merely" linearizable ones. Together with a previous result shown in [15], this implies that one cannot use the well-known ABD implementation of registers in message-passing systems to automatically transform any randomized algorithm that works in shared-memory systems into a randomized algorithm that works in message-passing systems: with a strong adversary the resulting algorithm may not terminate.