Okay, definitely a bug: going offline nukes my health in Horde.
To repro, I started a new horde life (just enter a new zone or change equipment) then immediately froze the feature with the cryo lab so that my HP is full. I then saved the game, closed the browser, then reopened the browser and started the game back up. Horde is still frozen, but I'm at 0.3% HP instead of full.
This also happens when the feature is not frozen, the cryo lab was just a clear way to confirm that something was fishy.