As things stand the edge of the map acts like there's an invisible wall around your territory through which only merchants, invaders, migrants and wild animals can pass. But since it's going to be possible for dwarves to go missing through accidents, or "accidents", why not add some more mundane sorts of disappearance?
Instead of coming to a halt as if their quarry had disappeared into thin air, hunter stalking an animal or a militiadwarf pursuing a thief or snatcher would follow their quarry off the map edge, possibly generating a notification. After that, a series of probability rolls would be made. For one of three outcomes: Return with animal corpse/item that was stolen, return empty-handed (with or without injuries) or fail to return. Relative skill levels, quality of equipment and so forth would modify these rolls one way or another, as would how many other dwarves were accompanying them; squads should bring the bodies of fallen comrades back with them, for example, and assigned work animals would at lreast have their fates known. Whether it was day or night, and eventually weather conditions like fog, could also influence the chances of getting back.
If the latter outcome occurred, the dwarf would be listed as missing. Ideally this would generate some kind of Search for Missing Dwarf job, its priority depending on how many friends the missing dwarf had, and with the searchers potentially meeting with some misfortune themselves. As for what happens to dwarves who fail to return, well, there could be several outcomes if they or their body aren't found. They could turn up again on their own after a random amount of time, end up as the spouse of a night creature, or even settle down in another site and turn up as a migrant years later. Sometimes, their fate would simply remain unknown unless the player subsequently stumbled upon the body as an adventurer.