What are the unique situations that allow salmonella to contaminate eggs?

Infected ovaries. In chickens, salmonella infection can localize to the ovaries and upper oviduct tissue and can be transmitted to the forming egg before shell deposition, resulting in contamination of the Albumin and yolk. Cooking the eggs until all liquid yolk is solidified kills the salmonella enteritidis.
Hens have salmonella. When hens have salmonella, the bacteria gets in the eggs. People can eat the eggs safely if they cook them well, and if they use good kitchen hygiene. Good food-preparation hygiene means not touching "raw" foods and then touching "cooked or prepared/served" with one's hands or utensils (must wash hands or utensils in between touching the "raw" and the "cooked").