Mr. Buffett, in particular, reached out to Mr. Cayne about a month ago, these people said, when the stock was approaching its one-year low of $100. While he is not known to be close friends with Mr. Cayne, Mr. Buffett might find more in common with the Bear Stearns boss than other Wall Street chief executives. Both in their mid-70s, they hail from the Midwest and are passionate bridge players.