Jamie Madrox takes on the memories and experiences of his duplicates; likewise he experiences their injuries and damage, though to a lesser degree. For example, when Proteus possessed and killed one of the duplicates, this caused Madrox Prime to collapse in pain. (According to Marvel.com this is due to "psychic backlash".) If a duplicate undergoes an injury, upon merging the merged Jamie typically ends up with an injury half as severe.
So it's consistent with the above that the death of a duplicate could have a severe but less-than-lethal effect on Madrox Prime. (That said, the authors have not been entirely consistent on this over the years, of course.)