To undergo the process of overripening where a fruit (especially medlars) softens and develops a special flavor as it decays slightly.
From French 'blettir', origin obscure but possibly from Old Norse or Germanic roots related to 'soft' or 'decay'. The term became specialized in English for fruit ripening.
Medlars are a wild fruit that literally has to rot a little bit to be edible—they 'blet' on the tree or after picking. Medieval English people actually valued this rotting stage as making the fruit taste like spiced apple!
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