Suppose I own many shares of the SPDR Dow Jones Industrial Average ETF Trust (NYSE Arca: DIA). How can I convert those shares in DIA into shares of the 30 components of the DJIA?
Yes it can be done, but not by small market participants.
The reason that ETFs that follow a market indexes so closely is because an arbitrage mechanism exists that allows conversion between ETF shares and shares of the underlying basket of securities. The prospectus of the ETF provides the details, but it goes along something like this:
A holder of 100,000 shares of the ETF can ask the ETF to convert them to the corresponding number of shares of the index that the ETF represents, and vice versa - a holder of the relevant number of shares of the index can exchange them for 100,000 shares of the ETF. This quantity is called a 'creation unit'.
If this mechanism is effective, then market participants can buy or sell ETF shares and convert them to index component and sell or buy them at a profit.