So with the original trilogy fresh in my head (just finished rereading tonight) along with SH, I'm fairly certain that Kelsier took over Marsh's body.
At the end of HoA, Marsh only has one eye spike, and we know 'Ironeyes' is still alive (or at least his body). Marsh also had the most Allomantic and Feruchemical spikes Hemalurgically implanted, so could technically be immortal, but Kelsier taking it over seems likely.