electricallight-fixturewiring
(Photo below). Is this safe?
Just a homeowner who has changed his fair share of fixtures and outlets… but have never come across this.
Two whites leading to the fixture white.
A red wire leading to the fixture black
And two black wires in the back that I don’t know where they’re going?
And bare wire (assuming neutral) just coiled up in there.
And there is burning/charring around the electrical box and inside the old fixture.
Is this configuration safe?
Most likely the second white and second black wires are the connection to the switch itself. If so, then what you've got is power line from circuit box to light, switch line from light to switch. (The alternate method is power line from circuit box to switch, switch line from switch to light - which would have been less confusing for you but he probably was dealing with old work by the sound of it.
How it works in your configuration (if I'm right) - imagine the electrical current like a flow of water. The power comes in from the breaker box on the black line (aka the hot line). The power then runs to the white line and down to the wall switch. When the switch is on it then runs back up the black line to the light. You connect black to black, and the power flows into the light, then out the white line. You connect white to white, and the power flows on down back to the breaker box, and out.
So - don't touch the second white and black. Just wire the light's white to the lonely white and black to black the same way.
Here's my best guess at the wiring based on the photo. Looks like you've got one hot/neutral coming into the box from the panel (or another switch/outlet), and you've got 2 hot/neutrals going out of the box to other switches/outlets. Since these are all joined together, it doesn't really matter which one is coming in and which two are going out.
Then it looks you you have a white wire connected to the bundle of hot wires, and that white is going out of the box to the switch, and then a black wire returning from the switch, which goes to your lamp. This is pretty common, but that white wire should probably be marked at both ends to indicate that it's actually a hot.
Based on what I can see in the picture, you do not have a ground wire. It's possible that the box itself is grounded, either with a ground wire screwed to it that's not visible in the photo or by metal conduit, but based on the yellowed insulation of the white wires, my guess is that your house is old enough that no ground was required at the time, so there is not ground wire.
Update based on your close-up picture, there are ground wires, they are sort of terminated to the box on the strain relief clamps. If you have enough slack, it would be good to wirenut them all together securely with one pigtail that goes to the box and one to your lamp. Otherwise, make sure they are all securely fastened to the box, only one of them (the one that leads back to the panel) is a "real" ground, the others are providing ground for downstream lights/outlets, so make sure that all all them are securely fastened.
Best Answer
I don't think that's really burnt...
The closeup of the red wire linked in the comment does not appear particularly burnt to me (it'd be a quite strange spot to have a burnt spot, anyway).
The setup is good
What this setup appears to be is a new-style switch loop that provides neutral at the switch box, which is now required by the NEC (so that fancy dimmers/smart-switches/timers/... don't have to pull dumb stunts to power themselves). The black wires that are nutted in the back of the box are the always-hots (incoming from the power source and outgoing to the switch), the red wire is the switched-hot coming back from the wall switch), and the white wires are all neutrals (incoming neutral from the power source and neutral off to the wall switch location).
One potential issue though
One thing I would check while you have this box open though is to make sure the grounds are made-up properly; the installer may have simply twisted the wires together without using a nut, which doesn't guarantee a proper connection. I would take all those bare ground wires, untwist them, add a ground pigtail to a 10-32 self-tapper (Garvin GSST or equivalent) driven into exposed metal on the fixture (this takes care of grounding the fixture), insert them into the correct size wirenut, and twist the wirenut on, so that you have them properly connected from here on out.