I'm looking for a U.S. stock with the symbol AULT from about 1999. How can I find information about delisted U.S. securities in general? Particularly historical stock prices, market cap, company name, etc.
You need a source of delisted historical data. Such data is typically only available from paid sources.
According to my records, AULT (Ault Inc) began as an OTC stock in the 1980s prior it having an official NASDAQ listing. It was delisted on 27 Jan 2006. Its final traded price was $2.94. It was taken over at a price of $2.90 per share by SL Industries.
Source: Symbol AULT-200601 within Premium Data US delisted stocks historical price data set available from http://www.premiumdata.net/products/premiumdata/ushistorical.php
Disclosure: I am a co-owner of Norgate / Premium Data.
In general you cannot. Once the security is no longer listed on the exchange - it doesn't have to provide information to the exchange and regulators (unless it wants to be re-listed). That's one of the reasons companies go private - to keep their (financial and other) information private.
If it was listed in 1999, and is no longer listed now - you can dig through SEC archives for the information.
You can try and reach out to the company's investors' relations contact and see if they can help you with the specific information you're looking for.