If the U.S. investors become net sellers of ADRs then the excess receipts are are sold back to the U.S. bank who will cancel the receipt and at the same time instruct the foreign bank to sell the equivalent numbers of shares on the foreign market. Sponsorship relates to whether the foreign company initiates the ADR market or instead accepts that someone else wishes to do so. An unsponsored ADR is one where a US broker. A sponsored ADR is preferable as the company is then subject to US reporting requirements and will pay the costs of distributing dividends and materials. With an unsponsored ADR the U.S. bank will recover costs from the movement of shares and dividends.
Less information is normally available on unsponsored ADRs.
There are in total more than 900 ADRs, representing securities from 40 countries.