Portable CB's that have cigarette lighter plugs work on a 12 volt (vehicle) system. You require a step-down transformer/adapter to use it inside your home. You can cut off the cigarette lighter plug if you like and wire it directly into your fuse box of your car, or use a female connection to your adapter. Alternatively, you might wish to purchase a base station which can just be plugged into the wall and another system for the car. You can pick these up rather inexpensively. The base station typically uses a stand alone antenna, which can be pricey.

I am wondering if it possible to find a CB Radio system that is not run off a cigarette lighter adapter for a vehicle? I am wanting to develop a small at home CB post just for local traffic if something happens here.
I know I could invest in a HAM Radio and I do have plans at some time in the near future to get one set up.
Is there a brand of CB Radio that is able to run off a standard wall socket plug? I was also thinking that if I do need to up and move quickly the CB would also switch over to a vehicle so I have a mobile comm system as well so it would serve a couple different roles.

I am new to the prepping thing and slowly starting to work on a bug out bag, due to my area, my plans are to bug-in as I'm pretty secluded so best chances would be for me to stay where I am.

CB base stations not only exist, but are quite commonnn in garage sales and online sites such as Kijiji...usually cheap. I got mine for I think $20.00, but I regret it. Personally, I would suggest getting a used portable model and a power supply. A 12 volt wall wart could be found for lless than a buck at garage sales I would bet. Cut off the barrel connector and test for polarity. Connecct to your CB power cord and you're good to go.

I am wondering if it possible to find a CB Radio system that is not run off a cigarette lighter adapter for a vehicle?

You could always just buy a 110Vac to 12Vdc converter with a cigarette lighter adaptor, so you can use you car CB in the house. This is on Amazon.com, but I'm sure you can get one on Amazon.ca, too: https://www.amazon.com/Converter-Supply-Adapter-Cigarette-Lighter/dp/B076ZP2P9N

If you buy a CB radio, it might be a good idea to get one that also receives the NOAA and Environment Canada weather channels. It's handy for receiving timely weather updates.

Years back I bought two Cobra CB walkie-talkies, one f them (model 38WXST) had the weather channels on it. I always keep that one in the centre console of the car in case of emergencies. It takes 9 AA batteries, came with an adaptor for the car lighter, and I bought a power adaptor to run it off a wall socket. I can use the little rubber antenna that came with it, or if I want, I can attach the cable of a whip antenna to it. The other walkie-talkie I use as a loaner for friends. They're pretty handy when you're out of cell reception range.

I operate my radio on 11 meters (in the 40 channels and outside) as a base station. I bought a power supply 30Amp from amazon. Also I use a full size antenna and in a good day that allows me to hear (in these low propagation, low sun spots) Argentina, in a couple years with more sun spots I should be able to hear Europa an Oceania.

Here in Canada CB is limited to 4 watts AM and 12 watts SSB. Amplifiers are illegal and for good reason.
On almost any given day I can turn on the CB in the truck and there will be some yahoo from the southern US blasting out anywhere from 100 to 1000 watts. This kind of power output causes splatter over close channels. For instance, if they are transmitting on channel 4 they will be causing interference from channel 2 to 6.
Sunspots do help AM DX i these frequencies. As an example, the 10 meter ham band is really not used right now, but I had contacts as far south as Colorado with only 10 watts back when the sun was more active. Without the solar activity, 10 meters is limited to almost line of sight.