emergency exit is apparently being blocked by sheer force, which shouldn't be this way, because according to the description of sheer force on bulbapedia (assuming it's correct because it has been proven to be as such with items such as eject button), "if (and only if) a move is boosted by the effect of Sheer Force, it will no longer trigger item or Ability effects that activate after attacking."
sheer force has been proven to block items such as eject button, because the description of eject button is as follows: "If holder survives a hit, it immediately switches out to a chosen ally. Single use." according to that on ps, which means that it only works after attacking.
however, the description of emergency exit is as follows: "This Pokemon switches out when it reaches 1/2 or less of its maximum HP.", which suggests that it does not only activate after attacking, which means that it ideally should not be blocked by sheer force
i've tested emergency exit to work regardless of golisopod being attacked, which can be seen in this replay:
http://replay.pokemonshowdown.com/gen7pokebankou-514351607
it shows that emergency exit works even when it is being brought down to under 50% via a status.
however, emergency exit is then shown to fail against a sheer force mon (in this example, nidoking), which can be referenced here:
http://replay.pokemonshowdown.com/gen7pokebankou-514353156
emergency exit did not work after being brought down to under 50% via a sheer force life orb earth power.