After a natural disaster, it's not unusual for government to set up curfews or issue Stay-At-Home orders. People caught driving or walking their neighborhood after curfew or in violation of Stay-At-Home are subject to immediate arrest and detention.
The only exception is Essential Workers. Naturally, people working as EMS, nurses, fire protection, or other essential functions are exempt and can move around (but only so long as they are working or coming/going to work).
What I'm suggesting is that, after natural disasters, there are a LOT of common essential functions that allow people to move about. Power plant workers, refinery workers, electricians, sewage & water treatment workers, trash collection, local broadcaster, etc... .
I've used this trick a few times and it works. Get someone you know from one of those types of work to print you an official looking letter on company letterhead stating that you are an "essential worker" and are required in order to maintain electrical, water, sewage treatment, power, communications, etc... for your county. Keep it brief, like 2 paragraphs at most. With an unreadable signature and an important sounding name at the bottom... it will pass the sniff test.
The national guard, if they pull you over, only have a minute or so to determine who you are and why you're driving at 10:00pm after curfew. They don't have time to make phone calls or check anything. If your "essential worker" letter passes the smell test... you can continue on your way to work. (note: this does NOT work if you have a wife and kids in the car, or if you are wearing shorts and sandals.) Look the part. Have a good quick story to back up why you are out so late or dressed the way you are. "Boss just called me to come in immediately. Plant emergency. Motor is out." is always good.
Get a letter like that (or two different ones if you want) before SHTF and keep them in your car or wallet. If sudden curfew and stay-at-home orders are announced, you may have SOME movement (don't push it) where others don't. That might allow you to see what's going on in your city or county. Letter in hand = get out of jail free card.
Heres a better idea. When the SHTF how about you just stay home and out of the way as they have asked you to do.
Depends on who 'they' are
You can also use the "Essential Worker" letter to get in and out of your city or county through checkpoints.
Keep in mind that the National Guard isn't necessarily familiar with your area, and they are operating on about 4 hours of sleep during an emergency. They don't know if your "power plant" has a substation in the next county that needs to be checked on. Make up a good sounding name for it... and it will sound reasonable to sleepy ears.
"I've got to go up the road 5 miles to the Johnsonville Substation to check on a tranformer and load switch". "I was ordered to check the Motley Pumping Station because sensors are detecting a leak. I think it's just a malfunction like last year, but we have to be sure." :>)
You can get around check points or even cross state lines if you can BS for about 3 minutes. Just keep it simple. Also, there's a built-in excuse why you don't know anybody's phone #'s, because everyone has to work from home. Your own boss is non-essential and isn't at the plant right now. You don't know who is in, because it's all on emergency basis. That way, stories are harder to check out.
If SHTF, you never know why you'd want to leave your city or county, but at least you will have the ability if necessary.