Stalkers, is a name given to the people that had to clean up after the Chernobyl disaster. These people, mostly soldiers, had to work almost unprotected in conditions of extremely high radiation. Obviously most of them died due to cancer and other radiation induced illnesses(some died after a few days, others lasted for a few years).
The term stalker was taken from the Brothers Strugatsky
book, "The Roadside Picnic". In the book, stalkers are people that enter areas which were contaminated by radiation(apparentlly because aliens landed there). Most of them don't live for long, and those who do suffer from mutations. For example, the main character's daughter is furry and has a tail.