Apparently, DNA polymerase can perform that function:
http://www.torna.do/s/Error-correction-during-DNA-replicatio...
DNA polymerase (DNAP) is a dual-purpose enzyme that plays two opposite roles in two different situations during DNA replication. It plays its a normal role as a polymerase catalyzing the elongation of a new DNA molecule by adding a monomer. However, it can switch to the role of an exonuclease and shorten the same DNA by cleavage of the last incorporated monomer from the nascent DNA.
https://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=tr...
DNA error correcting codes: No crossover.
DNA error correcting codes over the edit metric create embeddable markers for sequencing projects that are tolerant of sequencing errors. When a sequence library has multiple sources for its sequences, use of embedded markers permit tracking of sequence origin. Evolutionary algorithms are currently the best known technique for optimizing DNA error correcting codes. In this study we resolve the question of the utility of the crossover operator used in earlier studies on optimizing DNA error correcting codes. The crossover operator in question is found to be substantially counterproductive. A majority of crossover events produce results that violate minimum-distance constraints required for error correction. A new algorithm, a form of modified evolution strategy, is tested and is found to locate codes with record size. The table of best know sizes for DNA-error correcting codes is updated.