Can or will you be able to stake Cardano stablecoins in stake pools for rewards, such as Djed?
Let's first ask ourselves, what does staking really mean?
The purpose of the staking mechanism currently implemented in Ouroboros is primarily to incentivize honest real-time consensus on the Cardano Settlement Layer (CSL). However, the CSL is merely the first layer of a much larger ecosystem that facilitates the communication of globally interconnected DApps, also known as the Cardano Computational Layer, or CCL.
The CSL is the backbone and heartbeat of the system, optimizing for security and correctness over throughput, and was thus built first in a highly formal and concerted effort by for-profit companies. And so the protocol and staking rules are imbued with a level of rigidness that is necessary for a global base-layer.
The CCL can and will be a collection of diverse Hydra channels with unique consensus and ledger mechanisms. At first it will be a Cambrian explosion of channels/operators, all experimenting and competing with each other to establish network standards. Over time it evolves into a more stable and self-governing entity, eventually settling into some global equilibrium.
All of this is to say that the current implementation of staking on the CSL will be tinkered, built upon, and deployed in a vast array of ways both inside and outside the CCL. Sundaeswap's recent ISPO and World Mobile's Earth Nodes are examples of this, but are still only scratching the surface.
In principle, anything can be "staked" as long as the underlying incentive scheme is sound/sustainable.
In theory you could add stability to a PoS blockchain but staking tokens other than the core native token, but the underlying network has no concept of how valuable a token is. It can’t tell the difference between Djed and any old token you minted a billion of yourself.
In Cardano, PoS only works because ADA is valuable to someone. If the price went to zero, then the consensus mechanism would fail as well.