Could Accidental Intake Of Plastic Cause Toxic Fume Ingestion?

Hi, I made chicken breasts in the oven tonight for dinner and about halfway through the cooking process I began smelling something nasty, like plastic burning. I opened the oven and smoke poured out, I didn t see anything in the oven other than the food but kept smelling the unpleasant odor. A few hours after eating, I looked in the oven and saw what looked like residue. I removed it and it looks like plastic. My family and I ate the chicken, do you think it s harmful and are we in danger of toxic fume ingestion?