There is no law that I've ever heard of that requires an employer to pay you severance if they give you less than 2 weeks notice...SOME companies will pay you some severance when they lay you off, but they are the exception, not the rule. In most jobs, giving notice merely allows the company time to find a replacement for you, and in some cases, for you to train that replacement. I've done it both ways over the years.
I've given 2 weeks notice, and had the company fire me on the spot for it,
I've worked the full 2 weeks,
I've given less than 2 weeks with no "burnt bridge"
I've told my foreman "hey, at the end of the shift, I'm done",
told them AT the end of the shift, "Hey, I won't be here tomorrow...find some one else", and one time, I quit at the start of the shift, when they pulled some sh*tty stuff on the crew. "Hey, FVCK THAT! I'm outta here, call the hall and get someone else"...
That one I expected to be a bridge-burner, but a couple of months later, they had another job, and called and offered me the job...I declined, because I was working on a better job, but it was nice that they offered...
A lot depends on the particular industry you are in, and how hard you will be to replace...