Over the years, Fannie Mae and Freddie Mac showered riches on many winners: their executives, Wall Street bankers and Washington lobbyists. Now the foundering mortgage giants are leaving some losers in their wake, notably their shareholders, rank-and-file employees and, in the worst case, American taxpayers.

But even after the government seized the mortgage finance companies on Sunday and dismissed their chief executives, the companies’ outgoing leaders could see big paydays — a prospect that angers many investors, particularly because ordinary stockholders could be virtually wiped out.