Resistive memories are affected by significant error rates tied to structural relaxation and wear out of the resistive memory devices. A way to reduce the need for strong error-correcting codes (ECCs) is to improve error correction based on the weak bits, i.e., potentially faulty bits, identified in sensed memory words. Here, it is formally proven that conventional ECC decoders reinforced with weak-bit-flipping may achieve similar error correction capability as theoretical generalized-minimum-distance decoders. It is shown that weak-bit-flipping may reduce the uncorrectable bit error rate (UBER) by orders of magnitude when applied in conjunction with single-error-correcting and double-error-detecting (SEC-DED) or double-error-correcting and triple-error-detecting (DEC-TED) codes. In particular, weak-bit-information extracted from a 2T2R memory and used to reinforce a DEC-TED code with a conventional decoder may enable an UBER that is one order of magnitude better than the UBER achieved with a triple-error-correcting (TEC) code and a conventional decoder.