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The child has been identified as Titan Chandra Das, 14, from Brahmanbaria.
The mishap occurred on Friday morning.
SI of Badda Police Station Rahmat Ullah told bdnews24.com that Titon and other workers were asleep in a furniture shop when a wall came down on them.
Titon died on the spot, while another worker suffered minor injuries.
The child had been recruited as an apprentice by carpenter Abul Hossain six months ago. He, however, was paid no wages.