What is a "dead hand"?
"Dead hand" has a few different meanings. It's hard to tell just from that one sentence, but it sounds like the one you're describing is the case where somebody forgets to take a tile, so their hand ends up short tiles (it's also a dead hand if the player forgets to discard and thus has too many tiles). A dead hand cannot be used to win the round, but the player still takes their turns as normal until the round ends.

"Dead hand" also sometimes refers to a declared mahjong that turns out to be invalid (like above, that player cannot win anymore, and play continues), or a round where all tiles are drawn from the wall and nobody makes mahjong, but neither seems to be what you're referring to in this case