The Steem Dollar Problem

What happens if total existing Steem Dollars comes close to or exceeds the total Market Cap of Steem? That would essentially make the idea of "Trade your Steel Dollars in for a dollar's worth of Steem" impossible right? We may not hit that point, but it should be a discussed concern. Let's say after a couple of years there exists $1 billion worth of Steem Dollars. Let's say another social media sort of project comes along and takes market share away from Steemit so that Steemit's Market Cap falls to $500 million? (I'm assuming it will be above that sometime in the next 2 years)
At that point, Steemit users may start to panic and many will trade there Steem Dollars for a dollar's worth of Steem. However there won't be enough Steem in existence to allow all $1 billion of Steem Cash in the system to trade out for Steem.
Disclaimer: I am bullish on Steemit but see this as a necessary consideration. Right now there are a lot of blogs well over $1,000. I don't know what the total amount of Steem Cash is, but let's say it's just $1 million right now. So right now the Steem Market Cap can easily support a complete "Cash Withdrawal". My concern is that in the future we may hit a point where this is not true. And if that hits.. what happens? Will faith be lost in the project? What can be done to protect against that? Am I missing some point that makes this scenario impossible? (I hope I am)
The blockchain automatically issues however many Steem are necessary to redeem each Steem Dollar for $1 worth of Steem based on the 7 day median price of Steem. So, there can never be an insufficient number of to redeem all Steem Dollars. This is explained in more detail in the white paper.
I see discussion of rewarding liquidity providers but I don't see anything addressing if total market cap devalues below total Steem Dollars. Let's say there's only 1 Steem and it was worth $10. There is also only 1 Steem Dollar. That's fine. Now lets say the 1 Steem in existence drops to being only worth $0.01. How are you proposing the owner of the 1 Steem Dollar can exit the market and achieve lets say 1 dollar worth of BTC eventually? Are you saying at the point of his attempted swap to Steem, 99 new Steem will be issued.. and assuming the market doesn't realize there is this inflation they may go ahead and trade all 100 Steem for 1 Steem Dollar? Either that or you mean the Steem is created as Steem Dollars are? Not trying to argue but to understand. Where is this answer in the white paper as this goes beyond trade liquidity.
Even dantheman wrote basically the same thing.
https://steemit.com/steemit/@dantheman/steem-dollars-have-limits