Her body can be found in the back of the Super Duper Mart parking garage with her holotape on her corpse. Josh, two other unnamed minutemen and a settler are also found dead in or around the Super Duper Mart.
Emma's holotape, along with Josh's holotape, suggest the survivors of the Quincy Massacre, led by Preston Garvey, holed up in the Super-Duper Mart only to be driven out by a pack of feral ghouls, leaving three dead that Emma and Josh, returning from some errand, discovered. They were then killed by the ghouls themselves.
Emma, Josh and the minuteman found dead outside the Museum of Freedom are probably the three lost people referred to when Preston Garvey tells the Sole Survivor that "yesterday there were eight. Now, we're five." However, there is another dead minuteman in Concord in a backyard.