Copying information is vital for life's propagation. Current life forms maintain a low error rate in replication using complex machinery to prevent and correct errors. However, primitive life had to deal with higher error rates, limiting its ability to evolve. Discovering mechanisms to reduce errors would alleviate this constraint. Here, we introduce a new mechanism that decreases error rates and corrects errors in synthetic self-replicating systems driven by self-assembly. Previous work showed that macrocycle replication occurs through the accumulation of precursor material on the sides of the fibrous replicator assemblies. Stochastic simulations now reveal that selective precursor binding to the fiber surface enhances replication fidelity and error correction. Centrifugation experiments show that replicator fibers can exhibit the necessary selectivity in precursor binding. Our results suggest that synthetic replicator systems are more evolvable than previously thought, encouraging further evolution-focused experiments.