In some circumstances, dying immediately might be useful (such as if I want to be restored by revivify next round) so as to qualify as a dead creature instead of a dying one.
Is this allowed?
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As an unstable creature, you cannot do anything aside from rolling Death Saving Throws. Just like in real life, you couldn't just die, out of the blue.
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.
However, your teammates or pets or anything else can attack you to cause you to fail said Death Saving Throws.