Short answer is: In the current stage of Combat, you cannot drop below 1 HP from combat, anywhere.
Longer answer is: Yes, if you go unconscious you are stuck until someone helps you out, but currently the only way for that to happen is for something like... Door installation critical failing and damaging you into unconsciousness. I'm not 100% positive if you can genuinely push yourself below 1HP in that circumstance (or Hostile Atmo damage for example), but I know you definitely cannot drop below 1HP for combat.
EDIT: Additional relevant info: While at 1HP, you cannot initiate an attack, but will still fire back if attacked. Once you regen or heal to above 1HP, you may initiate an attack again.
“If you are conscious (HP > 0), you naturally regain HP without visiting hospitals or using other equipment via the equation: HP Regained / day = round(Maximum HP * .1)
If you are unconscious, then your body is totally unable to regain any HP and other medical methods will need to be applied. Any player can add an unconscious player to their party, and a Bacta Tank can be used to heal them above 0 HP.
Kay, many people have gotten knocked out due to trying to install a door at 1hp :p it doesn't happen often but it does when someone thinks they can install a blast door without failure and just got done hunting. I could have sworn that creature combat can be lethal, though? Was that changed?
As said before, short of a player taking non-combat damage, you cannot drop below 1 HP. I let a Kitin Strider wail on me for 2 days while sitting at 1 HP to make a point to a new recruit at one point in time.