Originally posted by @Sylvia B.:
My question is, why didn't the breaker trip?
Disclaimer: I am not a professional electrician.
You had a loose connection at that receptacle, probably at the terminal screw for the badly charred white wire (the top screw in the first picture, the right screw in the second picture). It might have also been at the small brass tab that links the two screws on that side of the receptacle - if it was damaged at some point, like somebody started to twist the tab off but then decided not to, it could also cause this problem.
The receptacle that you plugged the toaster oven into was "downstream" of this burned one. One set of white and black wires at the burned one came from the breaker panel, and the other set of wires went to the receptacle where the toaster oven was plugged in.
When the heavy load of the toaster oven (probably 15 to 20 amps) was put on the circuit, that loose connection heated up, and caused the melting and charring. The loose connection also limited the current that the toaster oven was drawing, which is probably why the breaker didn't trip.
If you had plugged in a small load (like a phone charger, or a
table lamp, or similar - much less than 1 amp), instead of the toaster
oven, you probably wouldn't have had this problem.
A GFCI probably wouldn't have helped you here, either. All the GFCI cares about is that all the juice that goes out on the black wire comes back in on the white wire. If any of the juice going out on the black wire goes somewhere else - like, through a nick in the wire insulation either inside the outlet or on the cord of an appliance, or into the water if you accidentally drop an appliance in the sink - then a GFCI will trip.
Some electricians like to "pigtail" the outlets. Instead of using both screws to feed power to the rest of the outlets "through" this outlet, they will run the wire from the breaker panel, the wire to the rest of the outlets, and a short wire into a wire nut. The other end of the short wire connects to one of the screws on this outlet. You can still have the same problem if the wire nut is loose (applying a load downstream will melt the wire nut), and you can have a problem at the pigtailed outlet if the screw for the short wire is loose - but only if you plug something into the pigtailed outlet.
Some home inspectors have a plug-in gadget made by Ideal or Fluke that allows them to find things like this. This gadget measures the voltage at an outlet, applies a heavy load for a short time, measures the (lower) voltage under load, and calculates the percent voltage drop. You can watch the measured voltage drop go up as they test outlets that are further along in the string from the breaker panel.
You can DIY this test with a voltmeter and
either a small space heater or a hair dryer. The voltmeter can be any
digital voltmeter that will read 120 V AC. It helps to get a 2-prong
plug with some cord on it (cut it off of a dead appliance), strip the
ends of each wire a half-inch or so, wrap each wire around one test
prod, and then tape it up really good with electrical tape - that way
you don't need three hands for the next part. Or, if your meter leads
unplug at both ends, get a replacement set of leads, cut off the test
prods, and wire the red and black wires directly to a 2-prong plug. If
you like gadgets, get a "Kill-a-watt" or similar plug-in meter online,
or at some hardware stores, for about $30 to $40.
Go to an outlet, plug
in your meter, and write down the reading. It's normal for it not to be
exactly 120.0 V AC, and it's normal for it to bounce around a few
tenths of a volt while you watch it. If it's consistently way low
(below maybe 110.0 V) or way high (above maybe 125.0 V), you may want to
seek help from an electrician before proceeding. Now, plug in the
space heater or hair dryer, and crank it up to high. Watch the voltmeter while you do this. It is totally normal for the voltage to
drop down when the heater/dryer kicks in, but let the heater/dryer run
for a couple of minutes and write down the lowest voltage you see.
Then, turn the heater/dryer off and do some math. If the voltage
dropped 5% or less (like, it was 120.0 V with the heater off, and 114.0 V
at its lowest with the heater on), then the circuit from the breaker
panel to that outlet is in pretty good shape. If it's between 5% and
maybe 8%, that's not as good, but it might be OK. If it's over 10%,
then you should investigate further, or have an electrician investigate -
you've got a loose connection somewhere between that outlet and the
breaker box, which is potentially dissipating a lot of heat inside the
wall somewhere. Back-stabbed connections, loose wire nuts, and terminal
screws that aren't tightened all the way down on receptacles and
switches can cause this problem.
Is that way more than you wanted to know about it? :D