Last summer, Mel Moomjean was unemployed and looking for a job as a sales director, but without meaning to he also applied for work as a receptionist, manicurist and fitness coach. His résumé, which highlights more than 20 years' experience managing sales teams, even landed at the beauty salon his wife goes to. It was looking for a stylist.

Gary Bauer, the salon's owner, thought Mr. Moomjean was joking. "I talked to his wife, and we had a good laugh about it."

It...