I currently have 3 fixtures in my house that have 6 bulbs in each fixture.
I don’t need the light they provide and desperately want to cut energy costs.
Do dead light bulbs consume any electricity if I leave them in?
Do empty sockets consume electricity if I just do not replace the dead bulb?
Thanks
No, they do not. No circuit, no energy used.
Just remove any bulbs you don’t need. A lot of older fixtures are set up for four to six small bulbs, and half that number of modern, low-power bulbs will give more light. No, dead bulbs and empty sockets don’t draw juice.
Fluorescent tubes and ballasts will draw some power even if the tube is dead, though.
Furthermore, leaving dead tubes in the sockets will wreck the ballast within a few weeks, IME. At work, I always try to change them as soon as I notice them. Swapping out a five dollar light bulb is a lot cheaper and easier than being lazy and having to replace the bulb and the $30 ballast.
Also, getting back to the OP, you leave the socket out, but that’s the equivalent of having bare wires hanging out in the open. Especially if someone wired it backwards and the threaded part is hot. YOU probably won’t do anything stupid, but you might have a friendly house guest who notices that the bulb is burned out and reaches into the fixture to grab it for you and gets greeted by an open socket. As a general rule, I don’t like sockets without bulbs in them.
Back when I first moved into my house, my half bath had four overly bright bulbs in the fixture. I just backed two of them out. It worked out nice because I left them like that most of the time and then would tighten them (to turn them on) when I was shaving.
an empty or dead bulb in an incandescent fixture uses no power.
if you unscrew a good bulb slightly, so that it is still held securely in the fixture yet off, that does leave a live open socket (a hazard).
Leaving a socket empty will also fill with dust and maybe a dead bug or two I’d say leave in a dead bulb.
If you do get dead bugs in there, *you can always dig them out with your finger, or a knife…
*please, don’t do this. I’m joking, and if you don’t realize I’m joking, you don’t belong anywhere near live circuits.
There are little screw-in plugs that turn a light socket into a 2-wire cord socket. I wouldn’t recommend actually using them for that purpose (they seem to date from the 1940s, when rooms had two wired things and no more)… but as safety plugs for unused sockets they’d be dandy.
Look on the bottom dusty shelf at your hardware store.
There might also be a standard rubber ‘crutch tip’ that would press into empty sockets and protect them. I’d have to stand around the hardware store doing weird things to figure out which size. 
they date from when electricity first came into the home. electrical light was a replacement for dangerous and troublesome gas or kerosene.
light bulbs tended smaller in power then. so you often had a drop cord light socket to bring the light closer.
you might have only or mostly light bulb sockets. people would use them for toasters, iron or radio.
some devices, or extension cords, might have a screw-in for a bulb socket instead of a plug.
You can buy them today at Lowes® if you want.
Dead bulb is cheaper.
We always used the light socket outlet thingies for Christmas lights. They worked great for that application.
Should bring this part up.
The technical part has been answered, but it probably won’t save you that much in electricity costs.
It’ll help, to be sure, but it just won’t be a big source of your costs (maybe a few dollars over the course of a year). Rather, you may want to check your appliances (not running the refrigerator full tilt or if you run the A/C or electric heating hard or the heated mode on a dishwasher, for example) and if there are tons of the little DC converter power bricks regularly plugged in but not doing anything.
Changing your A/C setting by a single degree will most likely have a more massive effect than going without electric lights entirely.