Here is a leadin to an article explaining self-correcting RNA (not DNA).
Unfortunately, I can’t post the full text, but what it amounts to is that poorly-duplicated RNA can trigger corrections to itself, as duplicating DNA does. This once more ups the amount of regulation involved in replicating living components. The summary I can post a link to says:
Mistakes can occur as RNA polymerase copies DNA into transcripts. A proofreading mechanism that removes the incorrect RNA is triggered by the erroneous RNA itself.
Such proof-reading mechanisms would contribute a fair bit to the stability of an existing pattern of life.