I need to begin with a frame challenge
You're trying to make a necessary game mechanic "realistic." Have you ever played the original Wasteland, the precursor to Fallout and basically the father of all post-apocalypse games? In that game death had meaning. When you died, the game started over.
And it sucked.
It was probably the one, single aspect of the game mechanics that people really hated. You had to go out of your way to save regularly, keep copies of the save files, etc., just in case you ran into something that gave you the beat-down of your life.
People aren't playing your game to experience reality. They're playing your game to have fun. And what you appear to not understand is that all the "rule breaking" easy-to-start-over aspects of modern games exist because people don't want to be punished for playing the game.
And that's what making death "really matter" does — it punishes people for not doing everything in their power to not have fun playing the game. And most players hate it.
Why is this frame challenge important? Because this question almost doesn't deserve to be asked here. There's a legitimate argument that your question isn't about worldbuilding. It's about game mechanics.
You need to make choices
Do I want to punish my players for not playing the game in exactly the way I think it should be played? (It's INCREDIBLY IMPORTANT that when you say "death really matters" you understand that what you mean is "I expect the game to be played a certain way." If you don't believe that, you're not ready to write this game.)
Do I want to make the game playable forever, or should I stick to the 60-hours of game play that's the average for a thematic story-driven game? Video game companies are increasingly hiring psychologists to help them design games that meet business goals. They want players to pay-to-play... over and over and over. It used to be you'd pay \$50-\$60 for a game and you'd expect about 60 hours of game play before the game ended. Today, people want to play forever. But dying sucks! And that's not how you make money. You make money by getting people back into the game ASAP.
Are you building a business or making a statement? I ran a micro-publisher for 10 years. I learned a lot of lessons. One is that there's a huge difference between authors who understand the business of writing and authors who are simply "developing their art" and don't think the nastiness of business should influence their art. The former tended to become profitable and popular authors. That later rarely became published. You want people to love your game, don't you? And yet you're talking about a game mechanic that sets them back. Have you explained (for yourself, if no one else) how that set-back encourages continued play? You need to really think this through, because people who must start over again and again stop playing very quickly. It is NOT a motivator. It's literally the reason why 99.9% of games make no big deal at all over dying.
Having said all that... let's answer your question.
Your player always starts with a special building: an automated hospital. The building may serve other purposes in terms of game mechanics (like supplying food for X number of resource gatherers, etc.), but it's primary purpose is to be the emergency medical team that gathers your player's body when it collapses into critical unconsciousness and puts it in suspended animation until all the necessary organs and limbs can be cloned to restore the player to health.
Your player is infected with a virus that forces the player into a death-like trance or meditation that fools attackers or waits out the environment while the virus goes to work rebuilding the body.
Your player actually dies. The body is out there rotting in the jungle or staring with a lifeless skull at the burning sun. What walks out of a cave filled with tech is a clone. Using an idea I first read about in Bob Mayer's Area 51 books, your character can wear a medallion or carry an artifact that is constantly transmitting his consciousness back to the complex to be used to fill the clone's brain with current knowledge. If you really want to make your players hate you, only fill the clone with the knowledge the player had gained at the last time the medallion was placed into the tech for download (clone has stats of "last downloaded condition").
At the moment before death, your player's tech activates an emergency teleport back to the hospital. Your player is stored digitally until everything is reconstructed, upon which the teleport is completed (the repaired body is rematerialized).
But, fair warning for future questions...
Frankly, I probably should have voted to close this question because it really isn't about worldbuilding at all. Your statement that "There is no overarching story-line to tie it into..." guarantees there is no worldbuilding going on here — just storybuilding, which is off-topic for this site. In fact, if you look at my proposed answers to your question, you'll see that none of them are about the rules and systems of a world. They're all about circumstances that rationalize game play.
However, making a game can involve a LOT of worldbuilding — the framework of imagination that the story (you didn't write) fits into that justifies all the game mechanics. I'm hoping you'll ask about those things.
So, fair warning to a new user: worldbuilding is about the rules and systems of your world independent of any story that may take place in it and it is not the development of game mechanics.
Please be sure you ask worldbuilding questions.