Ok. This is a weird one but hear me out. Leomund's Secret Chest has the following limit on what can be put into the small chest:

"The chest can contain up to 12 cubic feet of nonliving material (3 feet by 2 feet by 2 feet)."

So clearly, you are not meant to put living things into this secret chest. What about dead bodies? Does a corpse count as "nonliving" in this case? Which raises the question about the effect of Feign Death which states

You touch a willing creature and put it into a cataleptic state that is indistinguishable from death.

For the spell’s duration, or until you use an action to touch the target and dismiss the spell, the target appears dead to all outward inspection and to spells used to determine the target’s status. The target is blinded and incapacitated, and its speed drops to 0. The target has resistance to all damage except psychic damage. If the target is diseased or poisoned when you cast the spell, or becomes diseased or poisoned while under the spell’s effect, the disease and poison have no effect until the spell ends.

This may be a stretch of the bolded part of the spell effect, but would casting feign death on say......a gnome......cause the chest not to register it as living material and therefor allow it to be stored with in. 

Now I hear what you are asking. "Kaboom, why on earth do you want to store a gnome in a chest on the Ethereal Plane?" The answer, my dear forum viewer, is that I really don't know why. I am just curious whether Feign Death can be used to bypass the "nonliving material" requirement of certain spells. 

I find it unlikely that this would work, as "spells used to determine the target's status" probably is alluding to divination spell effects, but I am curious what the rest of you think. 

Thinking about it more, it becomes even less likely that it could be interpreted that way. For example, the potential stretching of terminology I was curious about would suggest that a necromancy spell targeting a corpse would work on someone under the effect of Feign Death as well, which obviously doesn't make much sense. In any case, just a funny thought I had, but the more I think about it the less viable it seems

An interesting question. It would ultimately be up to the DM, but I would think "appears dead to...spells used to determine the target's status" isn't meant to mean "spells that don't work on living creatures will work."

No. Leomund’s secret chest is not used to determine the status of the ostensibly non living material. It’s used to make a secret chest.

I want to say it works because the chest itself has to have a way to determine if the material is living or nonliving, although the spell doesn't say what happens if you try to put living material in it.

If this would be allowed either RAW, RAI, or I'm the DM deal with it, I can tell you exactly how to use it - Two gnomes trick a village into believing they are gods because they have a chest that can resurrect themselves if they die. They put a demonstration using Feign Death to appear dead, be placed into the chest, dismiss the spell, and come out of the chest alive.

This is an “ask your DM” issue. They just might allow it as RAF!

I want to stuff a gnome in a Leomund's, so I would allow it, but RAW, this doesn't work.

Quote from DxJxC >>

An interesting question. It would ultimately be up to the DM, but I would think "appears dead to...spells used to determine the target's status" isn't meant to mean "spells that don't work on living creatures will work."

Quote from Vince_Snetterton >>

Can you put a corpse in the Chest? Yes. Corpses are considered objects.

Can you put the target of Feign Death in a chest? No, because the target only looks like a corpse.

 I would probably have to agree that it doesn't work by RAW.

But it is somewhat interesting that something (dead or not) that can't be discerned due to the spell can suddenly be easily discerned just by trying to shove the "corpse" into a secret chest.

Quote from SexyDanger>>

I want to say it works because the chest itself has to have a way to determine if the material is living or nonliving, although the spell doesn't say what happens if you try to put living material in it.

Saying that the spell has to have a way to determine if the material or nonliving is like saying electricity has to have a way of knowing if a material is conductive or not before flowing through it or thermal energy has to know if the surrounding area is cooler before it entropies its way over there. Those interactions are a result of the laws of physics. They simply are.

There's a difference between a spell behaving a certain way when its target has a specific characteristic and a spell that directly tells you the target has that characteristic. It's the difference between a spell that tells me if something is flammable and a spell that sets flammable on things on fire.

There aren't a whole lot of applications for this aspect of Feign Death but it could potentially fool traps like a Glyph of Warding that are set to blow when certain creatures approach.

Quote from Thezzaruz>>

But it is somewhat interesting that something (dead or not) that can't be discerned due to the spell can suddenly be easily discerned just by trying to shove the "corpse" into a secret chest.

Light can be used this way too if the potential creature isn't Large. If it glows, it's an object; if it doesn't, it's alive.

Quote from InquisitiveCoder >>

Quote from SexyDanger>>

I want to say it works because the chest itself has to have a way to determine if the material is living or nonliving, although the spell doesn't say what happens if you try to put living material in it.

Saying that the spell has to have a way to determine if the material or nonliving is like saying electricity has to have a way of knowing if a material is conductive or not before flowing through it or thermal energy has to know if the surrounding area is cooler before it entropies its way over there. Those interactions are a result of the laws of physics. They simply are.

There's a difference between a spell behaving a certain way when its target has a specific characteristic and a spell that directly tells you the target has that characteristic. It's the difference between a spell that tells me if something is flammable and a spell that sets flammable on things on fire.

There aren't a whole lot of applications for this aspect of Feign Death but it could potentially fool traps like a Glyph of Warding that are set to blow when certain creatures approach.

Quote from Thezzaruz>>

But it is somewhat interesting that something (dead or not) that can't be discerned due to the spell can suddenly be easily discerned just by trying to shove the "corpse" into a secret chest.

Light can be used this way too if the potential creature isn't Large. If it glows, it's an object; if it doesn't, it's alive.

I disagree and feel your examples contradict each other but if it weren't RAW I'd allow it anyway because it's creative and doesn't break anything.

Quote from SexyDanger >>

I want to say it works because the chest itself has to have a way to determine if the material is living or nonliving, although the spell doesn't say what happens if you try to put living material in it.

If this would be allowed either RAW, RAI, or I'm the DM deal with it, I can tell you exactly how to use it - Two gnomes trick a village into believing they are gods because they have a chest that can resurrect themselves if they die. They put a demonstration using Feign Death to appear dead, be placed into the chest, dismiss the spell, and come out of the chest alive.

 
I mean... you could just use an ordinary mundane chest for that and just claim it's magical. No need to involve a chest that can vanish.