I'm referring to damage from falling from a height, but also from when a character falls on their face when they become unconscious. Does a saving throw or other mechanism exist to handle equipment damage from a fall?
Are potions and breakable things carried by a character broken or damaged when a character falls?
There are no rules for this. The general assumption seems to be that your equipment will not break when you fall or become unconscious.
This is also true for being targeted by spells, which specifically mention they don't affect carried or worn objects.
If you want to introduce this into your game, make sure to inform the players beforehand how it is going to work, as this will change how they deal with the items they take into battle with them.
5\$\begingroup\$ I'd add to this answer that implementing this house rule might be a bad idea, given the number of times where potions and other delicates items would realistically break when adventuring, thus having to roll really often, and potentially breaking the session pace. If OP is curious about this, it might be worth creating a new question about the potentials flaws of this custom ruling. \$\endgroup\$– ZomaMay 17, 2021 at 8:05
2\$\begingroup\$ @Zoma that depends entirely on how you implement it, I think the warning is a bit too blanket to say that all such house rules would be awful. But yes, if OP wants a houserule and has decided on one, dedicating a question to it might give them some pointers :) \$\endgroup\$– ErikMay 17, 2021 at 8:29
\$\begingroup\$ I don't have a rule, I wanted to learn from existing rules from others so I'm waiting for someone to give me examples of that being implemented. \$\endgroup\$– TomaMay 17, 2021 at 9:16
7\$\begingroup\$ You didn't ask for that, so I doubt anyone will post their own houserules for objects taking damage when falling. I'm also not sure if this is the right site for such a question, though. \$\endgroup\$– ErikMay 17, 2021 at 9:40
2\$\begingroup\$ @Toma I don't have experience with this, but you might link it to damage taken, like for every 10 damage taken in a fall, one fragile item breaks. But honestly it seems a bit like rubbing it in -- the character already fell (embarrassing and often holding back the party) and took damage (ranges from annoying to very dangerous), and now they lose equipment that is potentially very valuable or necessary for class functions too? \$\endgroup\$ May 17, 2021 at 14:21
No. Potions are objects, not creatures, so they don't take damage. See p183 of the PHB.
A fall from a great height is one of the most common hazards facing an adventurer. At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall.
In terms of why, in games where we have had to track the health of each item you carry it gets super tedious. It's enough effort to track my character's abilities, I and other players I've played with have found it annoying to track the HP and such of every item we carry.
5\$\begingroup\$ AD&D's old breakage rules were just a saving throw. They either broke or where fine. There was no health tracking. It was a pain to roll and generally a bad idea (any area attack could destroy some potions, wands, scrolls), but at least you didn't record how many HP each potion had left. \$\endgroup\$ May 17, 2021 at 15:35
No, they don't. As stated by Nepene Nep they do not by the rule book and it would be too tedious if they would.
Besides in the DnD universe adventurers would pack bottle and other breakable stuff so that they can survive impacts that are expected like from fights, long falls, being thrown against wall etcetera. Bottles and such will have rope or other material around it to protect it.
I would let them be 'indestructible' as they are now.