Equity actually declines, but of course, the stock itself becomes more valuable. I was surprised to learn this.
Stock Buybacks
When a company buys back stock from the public, it is returning a portion of its contributed capital to shareholders. Those shareholders are literally cashing in their equity. As a result, total stockholders' equity declines. It's important to note, however, that the remaining shareholders -- those who didn't sell their shares back to the company -- don't really "lose" anything when equity declines through buybacks. After a buyback, there is less equity in the company, but there are also fewer shareholders with a claim on that equity. In fact, by reducing the supply of company stock available in the market, buybacks tend to push share prices up, which leaves the remaining shareholders with stock that's more valuable than before.
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