People usually do that to specifically indicate that it has a problem of some sort, so someone else doesn't assume it's working. Although with a toaster, just the act of flipping it around to cut the cord might dislodge whatever toast bits were causing it to smoke and such in the first place.
In my experience, desperate people cut the cords off of perfectly good appliances to sell the copper as scrap. Copper wire fetches something like ~$1/lb as scrap. It's infuriating when they cut it right at the connection to the appliance, making it too time consuming to test.
A label of "Broken" or "Works" or "Missing X" is so much more helpful for appliances left out.
Good point, if it was just sitting by the curb, a metal scraper might have just cut the cord instead of taking the whole thing. I've noticed that different scrapers have different criteria for what they'll take. Some will take the whole thing and break it down or just sell it as unsorted metal and others are more particular and will pick through and just take what they know they can get the most/easiest money for.
People usually do that to specifically indicate that it has a problem of some sort, so someone else doesn't assume it's working. Although with a toaster, just the act of flipping it around to cut the cord might dislodge whatever toast bits were causing it to smoke and such in the first place.