In a stupid, foolish, or silent manner; without speaking or without intelligence.
From 'dumb' plus adverbial '-ly' suffix, meaning 'in a dumb way' or 'in the manner of a dumb person.'
The word carries both meanings of 'dumb'—it can mean silently (not speaking) or stupidly (lacking sense)—so 'he stared dumbly' works whether you mean he couldn't speak or he didn't understand.
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