The rules on dropping to 0 hit points (PHB p. 197) almost entirely depend on taking damage. The section begins as follows:
When you drop to 0 hit points, you either die outright or fall unconscious, as explained in the following sections.
However, we then have the two following sections which make reference to dropping to 0 hit points:
Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.
If damage reduces you to 0 hit points and fails to kill you, you fall unconscious (see the appendix). This unconsciousness ends if you regain any hit points.
In fact, the only reference which doesn't include the condition of damage pertains to monsters:
Monsters and Death
Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.
The only rule pertaining to player characters which doesn't involve damage is what happens after one is at 0 hit points:
Death Saving Throws
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.
All emphasis mine. All of this raises the following question: in the absence of assuming intent (however clear it might seem), are there any rules for determining what happens to a player character who drops to 0 hit points as the result of an event which does not involve damage, such as the expiration of the aid spell?