I know several people who got jobs in industry, doing work entirely unrelated to the topic of their Ph.D. theses (and to anything else they learned as students). The people who hired them seemed to have the attitude that they want to hire smart people who can learn the relevant background information reasonably quickly, can understand the problems they should work on, can make a real contribution to solving them, and can communicate effectively with other employees (not just with other mathematicians). The Ph.D. degree in mathematics strongly suggests (though it doesn't strictly imply) that one has at least some of these qualities. Letters of recommendation and interviews add more of the desired information (or of its negation).