Electric oven? Our electric oven coil caught fire and it didn't go out until...

Our electric oven coil caught fire and it didn't go out until we unplugged it. Does this mean we own to get a whole strange oven or can we replace the coil?
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That depends upon what actually was burning. Without seeing the oven, I can just make generalizations, so here go.

Ovens are basically a large metal box. Every component contained by the oven is metal. It's unlikely that the heating element is what be burning, but rather accumulated grease and food. My guess is that your oven requests a good cleaning.
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If the coil actually has a "hole"contained by it, you can just replace the coil. It's actually a fairly easy job. Usually a couple of screw where the coil plugs into the back of the oven and you slide the infirm one out and put the new one in.

If it caught fire because it be dirty, then a good cleaning should help yourself to care of it.

From your explanation, it sounds like the coil be the culprit because if it was soil/food/junk burning, it would have kept on burning even after you cut the power to it.

I have that happen to me once! Christmas Eve afternoon, baking pies; scared the caca outta the kids! Looked close to someone light a big sparkler in the oven! Thank God, I didn't own any pies in there on the other hand!
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Answers:    Since the fire didn't go out until you unplugged the oven it's probably the element. To replace first unplug the oven. There are usually 2 nuts at the backside of the oven which hold the element in place. Remove them and verbs the element out a few inches and you should see the 2 wires that need to be unplugged. It's easier if you use nozzle nose pliers. Take the old one to an appliance store and attain a replacement.
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You should be able to buy a replacement coil but, I own to ask, did the coil catch on fire? or did food stuck to the coil burn? I'm figure it was food, the coil may still be good. Clean it and try it.
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I would THINK lately the coil.But why did it catch fire? I am guessing it is the lower Bake coil.Remove it , then turn on the Broiler coil(upper) to see if it works.If it DOESN'T,next the whole oven might be blown.