Stringers are not illegal, keeping fish alive in your possession is. When you see this happening, phone the local conservation office immediately if possible. Two summers ago, the Squamish was closed immediately right after the Cheakamus chemical spill. The local CO caught several anglers not only fishing in a closed water, but also having several live pink salmon on a stringer. Most people who keep fish alive while in their possession is attempting high grading, meaning if they get a larger fish, they would release the one that is already in possession. High grading and other violations are explained in the Freshwater Fishering Regulation Synopsis:
http://www.env.gov.bc.ca/fw/fish/pdf/fish-synopsis_2007-08_general.pdfKeeping your dead fish in the water on a stringer is legal, but there are things to watch out for. In a cold lake, it is a good way to keep your fish fresh. In the Fraser River, having your salmon in the water around late summer is not a great idea. The water temperature is too warm and that usually results in spoiled meat. It's best to have a cooler with you in this case.