Charles Ponzi, in 1920, was in a different situation, compared to an anonymous bitcoin environment. He ran his scheme to the very end, went bankrupt and into jail, because he could not run away and disappear. He served drinks to his "customers", who were staging a bank run and gathering at his door, just to extend his time of fame by one more minute.
But now let's look at the personality of a (still hypothetical) Ponzi scheme operator. (I'll call him "he" for simplicity.)
We know some of his personality traits pretty well. He lacks law abidingness. He is extremely greedy. He must be an excellent liar. He must be thoroughly anti-social. He must be somewhat intelligent. (If he were highly intelligent, he probably would not have to resort to crime to make a good living.) In short, he is a low-life form you don't really want to share the same planet with.
Now let us look at how a Ponzi scheme ends. At first thought, one would think that it ends when interest exceeds new deposits, but it is not so. In fact, forget about interest. Think about the actual heap of money the Ponzi scheme operator has collected.
He will continue running the scheme as long as that heap grows. But, of course, growth will sooner or later stagnate and make way for some random sequence of growth and shrink phases, as "investors" withdraw some or all of their gain.
That is the time when an intelligent Ponzi operator will shut down and run with the money. However, greed may get in his way. He will hope to rake in a million of dollars, if he could just bridge this problem period and convince more newcomers to part with their money.
He will do anything to make that happen. He will keep promising totally unsustainable yields, he will accept any new "investment", no matter what, he will try various kinds of publicity stunts, even bets he is sure to lose.
However, at some point even the stupidest "investor" will realize that, assuming that at some time a Ponzi scheme amassed, say, BTC100,000, at 7% per week there would be BTC10million just 1.3 years later. BTC10m? Where would these come from?
So sooner or later the "investors" will attempt to withdraw. Some will do that anyway, because they want to buy a new car or a new house. The early "investors" should have amassed a neat stash after a couple of months, many times more than their original "investment", so the tendency to withdraw grows by the day.
Needless to say, the amount of money actually available in a Ponzi scheme is tiny, compared with the amount the scheme owes, so even a trickle of payouts will quickly make its operator very nervous.
Sooner, rather than later, the Ponzi scheme operator will realize that the millions of dollars he hoped to rake in are unattainable, and he'd better be content with what he has, so he will disappear. Perhaps he will make some moves before that, designed to stall and confuse the "investors". He might state that he sold or gave away his business, he might pretend he got sick or died, he might do confusing deals with sub-contractors, he might invent maneuvers I cannot even think of. But ultimately he will cease to pay up, and that will be the end.
Now let's look at the currently ongoing Ponzi scheme. After the discussion here, new "investors", even the most gullible ones, may have become a bit weary, so we may currently experience a phase of stalling new "investments". Whether this is enough to let the bubble burst, remains to be seen. In the most Ponzi-favorable circumstances, i.e. no big withdrawals and a very optimistic (or greedy, to be more precise) Ponzi operator, willing to risk much of his accumulated stash, the scheme may weather this storm and carry on, but how long would it take for the less optimistic "investors" to run for safety and withdraw? After all, they could withdraw their money, wait for just a month or two, and if the "business", against all odds, survives, come back and "reinvest". At least some people believe that only the first very few withdrawers will actually see their money, so a withdrawal now would be the safest path to riches. My personal guess is weeks or a few months. A year should be out of the question because there aren't enough bitcoins in existence to make it believable, even for the mathematically challenged.
And don't think that he could just lower the interest rate. If he did, more people would withdraw their money. It's a one-way road, and not a long one.
