I don't think people would do this at scale, even today. Suppose I have $30,000 that I want to keep cash (either physical, or a bank account). If I were to keep this at home, I would want to insure it. I can't find what this insurance would cost [0], but jewlery insurance seems fairly comparable, and comes in at about 1-2%. This means that a negative interest of at least -1% is still cheaper than insuring the cash under my matress. Add to this the general convenience factor, and some distrust of insurance companies, and they could push the rate even lower than that.
While there are plenty of individual households that would probably make the decision to store money under their mattresses in a negative interest rate environment, those households are not where most of the cash is. In general as an entity (be it individuals or bussinesses) have more money, they become increasingly aware of the costs of having many.
A convenience store that has security cameras fixed on the cash registers; reguarly has a manager cycle cash from the registers to a safe, and hires an armored car to transport cash to the bank is well aware that keeping cash as physical cash is not free. It is nice if the bank pays you to keep your cash in a bank account; but if the bank decides that you need to pay a reasonable them to keep your money safe; that is a price that most people (when weighted by the amount of money they are handling) would be willing to pay.
The threat of storing money as physical cash still puts a lower bound on how low interest rates could go; but that is far below 0%
In practical terms, I suspect it would be politically untenable to expose negative interest rates to individual savings accounts, but even a "small" subsidy allowing individuals to maintain personal savings accounts up to, say, $250k would still maintain most of the economic goals of a negative interest rate without the political backlash.
[0] Not that cash insurance isn't a thing, but you need to submit actual information to get a quote from anyone.