If the loss of stake is less than the cost of the proof-of-work, then there is a gradual transfer of the ownership of the coin to the mining farms and thus the stake eventually becomes winner-take-all concentrated.
The point is that proof-of-work is no matter how you organize it, a transfer of wealth out of the ecosystem to pay for security. And worse is that unless your coin is the "one chain to rule all the others" then your coin is always vulnerable to rented double-spend attacks, because even if your proof-of-work algorithm has been implemented on an ASIC and has great investment in mining farms which do not wish to destroy their investment by renting out hashrate to attackers, the problem is they effectively control the coin (even in your negative interest rate design) because they can decide to move their hashrate to the coin which they feel has better attributes or is a new pump&dump speculation (moving on from one to the next).
Thus your undesirable negative interest rate on savers is an insecurity. It creates a power vacuum for the miners to move their hashrate to a coin that doesn't have that weakness and to 51% attack and short your coin on the way out the door.
Proof-of-work is a winner-take-all, "the one chain to rule them all" phenomenon. Slice and dice it as you wish, that won't change.