I've been thinking about the injuries system a lot over the past few weeks. Having played X-Com, Xenonauts, XCOM: EW, XCOM 2:WotC after it went on sale and beating them all this month, I've come to a few ideas that might all be beyond scope.
Injuries aren't interesting unless you can purposefully inflict them (ie, aiming for the legs to stop someone from running away) which is very Fallout and I kinda have my doubts that any such system would really be used. Save for the times when you'd want to capture an alien, you'd always just be aiming to kill rather than to maim. On the other side, for the players, an injury system is only as good as your ability to interact with it. A simple way to do this is to have individually armored locations such as helmets and leg pads. Each of these would provide some kind of trade off such as reducing aim, vision, or mobility.
There is a much more interesting and difficult to do variant that I've thought of though: having injuries be effectively permanent. A soldier who got blasted in their dominant hand with superheated plasma could get nerve damage which lowers the aim of anything that uses that hand for seemingly the rest of the game. Someone could have their off hand melted by a plasma grenade meaning they could only ever use it to hold a shield effectively but take large penalties for two handed weapons. Eyes can be lost and vision can be fried.
Cuts and bruises and concussions can be fixed at the beginning. Only later on, when you've stolen some sibilian stem glands that you can repair the simple things like nerve damage.
Even better, and this is the real crux of this idea, is that soldiers who are downed are only rarely dead. Someone could lose both their arms because of a stray rocket or need to have one of their legs amputated because the plasma just melted too much of the limb. Not dead, but might as well be dead to you since they're no longer useful as soldiers.
Enter Alien Electronics: In Xenonauts 1, there was the officer in charge of the barracks who was missing an arm. With the first range of base upgrades he got a rather basic replacement, with the second he was sporting a functional cybernetic arm. While I wouldn't want X2 to go full MELD, being able to revive 'dead' soldiers the further the along you are in the campaign would feel absolutely stellar. You may have lost your 90 Aim sniper half-way through due to an accident that stole their sight, but they're still with you. Psionics can let someone see through cameras, or better yet, be able to only see aliens while the rest of the non-blind squad gets the scouting information that lets them know where to go. Even if they can't attack robots anymore, they can be used again when the technology is there. It's just expensive is all.
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This can lead to a very silly situation where most of your squad is a ragtag bunch of raggedy anne soldiers with the worst scaring anyone has ever seen. No idea if anyone wants that.