As more money pours into index funds, those index funds need to purchase more shares of stock which are part of the index being tracked. Is it possible that an index fund will be unable to track an index because it is unable buy more shares of a particular stock? If so, what happens?
For example, across all index funds, is it possible that the total amount of money weighted to a stock issued by company X exceeds the market capitalization of X.
The total amount of money weighted to issued stock can not exceed the market capitalization because the market capitalization IS the value of issued shares.
What you are referring to would be a case of a highly illiquid stock, one that probably doesn't belong in an index fund. If an index fund cannot buy shares, that means there are no sellers, which means there isn't really a market for the stock.
Markets are made by buying and selling activity and 99.99%+ of the time there are both buyers and sellers.
Think about it from the perspective of an individual investor. There is almost always a price at which someone is willing to sell. If you bought AAPL at $200, there is likely a price you would be willing to sell those shares. It may be $300, $500, or $1000, but there is a price. Obviously, this is an extreme example and highly liquid stocks tend to have much tighter spreads (difference between bid and ask prices).
Also, keep in mind that index funds sell positions as well.
If you refer to Michael Burry statements about the ETF bubbles and assume that everyone will go buying index ETF.
Logically, I think it is impossible
In fact, what Michael Burry is worry about is the index fund become the hand that pushing the index itself. IMHO, this is somewhat impossible, as a prudent investor should spread their portfolio and hunt for underperformed company stock.
However, this doesn't mean it will not happen, i.e. this is indeed a serious issue in the immatured emerging small country market. This is not happening to those country index fund, but to the small country sovereignty fund Price Keeping operations (PKO, a synonyms abbreviation pun to United nation Peace Keeping Operations). I.e. that sovereignty funds bureaucratic will systematically apply an algorithm to "stabilise" the index.
is it possible that the total amount of money-weighted to a stock issued by company X exceeds the market capitalization of X.
It already happens. Indeed, people will attempt to buy in-advanced on potential gains. Thus you will see some hot company stock trade under very high Price earning ratio. Nevertheless, it cannot goes up indefinitely.
You're asking what happens when the demand for an item outpaces the supply.
The price of the item (in this case, the prices of the underlying stocks) rise until an equilibrium point is reached.
Even though the number of shares in a particular company is (in the short term) fixed and finite, the market value of those shares can increase without any bounds if enough people are hell-bent on investing in the company (no matter whether this is because they're index funds or for other reasons).
For example, suppose the current market capitalization of Acme Corp is $1 billion, and there are new investors who have firmly decided to invest $2 billion in Acme, come what might. The resulting scramble to buy shares quickly causes the share price to double, raising market capitalization to $2 billion. All of the new investors get to spend their money on Acme like they wanted to. The previous shareholders sell everything and make a killing -- or if some of them don't, that just causes prices to climb further until the market has absorbed the inflow of money.
(Some of the new investors might have gotten in early enough to buy at the old share price. After the price increase they find that they now have more money in Acme than they decided to have, so they happily sell some of their shares at the new higher price to rebalance, making a profit).
