Automatic Strategy Tasks with "In Error" status - will they remain "In Error"?

Summary:

Automatic Strategy Tasks with "In Error" status - will they remain "In Error"?

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In the last 10 days on PROD, the "Send Dunning Letters" job has errored after 23C was applied, resulting in about 20,000 Strategy Tasks ending up with an "In Error" status like this:

My question is - will those Strategy Tasks remain with an "In Error" status permanently?

Ideally they will, because the customer I am supporting does not want the Strategy Tasks to suddenly be completed at a later date as that will result in lots of reminder letters being sent out, which are no longer required.