Don‘t Starve is very close to what you are describing. At any given time you are about a day or two away from dying and you spend almost all of your time trying to push the threat a few more days forward. In addition to the short term problems like finding food and shelter, Winter is always looming off in the distance so you have to be preparing for that as well.
Its not my favourite game, but it manages to maintain a baseline level of danger throughout the entire game which similar games do not.
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