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The fourth level of exhaustion imparts this effect on a creature:

Hit point maximum halved

The Basic Rules make it clear that whenever you divide a number for any purpose, you round down:

There’s one more general rule you need to know at the outset. Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater.

Most Challenge rating 0 animals have a single hit point, so when these creatures reach the 4th level of exhaustion, they would presumably be left with 0 hit points and die before reaching rank 6. Is this correct?

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The creature's maximum hp would drop to zero, as you say.

When a creature's maximum hp drops to zero, its current hp will also be zero, so it will start making death saving throws (see rules here):

Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life.

It's possible the DM might decide the creature does not get death saving throws. If the DM does allow death saving throws, then the creature can become stable:

A stable creature doesn't make death saving throws, even though it has 0 hit points, but it does remain unconscious. The creature stops being stable, and must start making death saving throws again, if it takes any damage. A stable creature that isn't healed regains 1 hit point after 1d4 hours.

The "regains 1 hit point" won't happen, but it looks like the creature could remain stable for some time -- either until its exhaustion level increased due to lack of food and water, or until its exhaustion level decreased due to rest or medical attention.

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    \$\begingroup\$ Coma - it's not just a movie from the 70's. \$\endgroup\$ Apr 10 at 12:35
  • \$\begingroup\$ While this is a fine answer and a valid way to rule it, this is really just rubbing up against a scenario the rules weren't designed for -- the exhaustion rules are designed to work for player characters, who are assumed to have many hit points, and have weird effects when you get too far outside that realm. \$\endgroup\$ Apr 11 at 1:15

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