[RPG] Can Leomund’s Secret Chest be summoned while it is not prepared

The death of the caster does not cause the spell to end. To start with, the spell is instantaneous. You cast it, a chest is hidden, and the spell is done. However, the spell lists all the ways it which its effect can end:

After 60 days, there is a cumulative 5 percent chance per day that the spell’s effect ends. This effect ends if you cast this spell again, if the smaller replica chest is destroyed, or if you choose to end the spell as an action.

So the caster dying will not end the effect of the spell. However, only the caster can use the replica to recall the chest from the Ethereal Plane. The spell (like most spells) consistently uses "you" to refer to the person who cast it. In fact, the entire chapter on spellcasting uses "you" to refer to the caster.

That being the case, while the effect of the spell does not end with the caster's death, the larger chest is, for all intents and purposes, lost forever as soon as the caster dies. There might be one way around this, though. The chest is only "irretrievably lost" once the effect of the spell ends. Until that point, it is hidden on the Ethereal Plane. While the nature of that hiding is unspecified, it certainly seems possible that you could travel to the Ethereal Plane and look for the chest there.

It lasts reliably for up to 60 days after the casting of the spell, regardless of what you do with it after

The relevant paragraph from Secret Chest (which is Leomund’s Secret Chest without the Leomund) is

After 60 days, there is a cumulative 5 percent chance per day that the spell's effect ends. This effect ends if you cast this spell again, if the smaller replica chest is destroyed, or if you choose to end the spell as an action. If the spell ends and the larger chest is on the Ethereal Plane, it is irretrievably lost.

This paragraph mentions no condition for the cumulative daily failure chance, so it is unconditional. The simple fix for this is to regularly recall your chest and cast the spell again and making sure you keep your chest on the material plane if you expect that you won’t be able to cast spells, have access to your replica or have any spare 4th level spell slots for a long period of time (although such circumstances should be rare enough that it may never come up in any campaign you play in, but it’s worth keeping in mind if you decide to travel to other planes like the Feywild that may have a different concept of time); Keep in mind that the spell doesn’t consume its expensive material components so it only costs you another 4th level spell slot to do so.