What a mess. I'm glad that you were able to peel off the plastic. I have a very old electric stove but I do keep burner covers on it. In the past many of my previous roommates would just turn on one of the burners without removing the burner covers. I kept telling them to just remove all of the covers before they turned anything on. So many covers were melted and they also smell like burning plastic. Now I live alone so unless one of the cats does something I shouldn't have any more of these problems. I usually only use the oven now and I use the microwave oven for everything else.

On a slightly different note, quite a while ago I noticed a plastic burning smell when I was driving. It turned out that some thick plastic got stuck under my car and it melted. I had to take the car to a gas station near my work and the man had to remove it. At first he said that it might just have to burn off but when he looked at it more closely, he said it would take a long time for it to burn off. Now every time I see a plastic bag floating around while I'm driving, I make sure to avoid driving over it.