The primary reason to have a "floating supply" is to maintain price stability even if the supply/demand ratio changes.
There were already some experiments in the cryptocurrency space trying to create a sort of "peg", where the value of the currency is meant to be stable but the supply is floating. Most of them feature a blockchain with two or more types of currency.
I want to present an older "stablecoin" called
NuBits to explain the problems and challenges with this approach. NuBits works with two currencies, NuShares and NuBits. NuBits are meant to be stable, but with floating supplies, while NuShares have a deterministic supply but a free-floating price. In times of more demand, NuBits are created; while in times of less demand, NuBits can be "parked" (locked) so the freely circulating supply decreases, and the "parkers" are rewarded with NuShares.
BitBay, which was already mentioned, afaik uses a similar model.
The problem with these systems is that the supply does not
really float but instead it increases all the time, because the "parked" coins are only temporarily locked away. In a long bear market the whole system can become caught in a "death spiral" where all assets depreciate and there is no longer an incentive to hold the peg.
A newer, interesting approach I just discovered today (and the primary reason why I'm answering here) is
Basis (still in alpha, afaik). In this system an "oracle" monitors the price of the coin with respect to the USD. If the price goes below 1 USD, then a "bond" is created and auctioned. The coins given out for this bond are destroyed. When the price goes above 1 USD again, coins are created and the bond is converted into a coin (with an 1:1 ratio; that means if you bought a bond for less than 1 USD you can make profit).
Sounds quite similar to NuBits, or not? But there is a crucial difference: Bonds have an expiry time. If they expire they simply are destroyed.
This system seems better thought-out than NuBits because
supply here really can decrease. However, its better incentive structure has a price: "Bonds" buyers can lose all their investment, if something goes wrong. (BitShares, afaik the only coin with a peg that really held it until today, has a similar characteristic, but it works differently - the post is already long enough, so I'll not expand here).
So the question DooMAD raised about "
how to decrease supply" (in times of economy/demand contraction) has an answer: It can most likely only be decreased if some people are ready to risk to
really lose something - for that to happen, they must get an interesting reward for it. I don't see that as a real problem: we have a financial system where margin trading is pretty popular, so the
target audience for risky financial products exists and a Basis-like system could find its place there.