A decent amount of states in the US have “at-will employment” laws, meaning you can be fired for any reason (excluding specific things to do with “protected classes” like race, etc.), at any time, with immediate effect and without any notice. Similarly, this means you can quit your job at any time, with immediate effect and without any notice. If you quit, it’s only if you want to maintain reputation or relationships that you should work a notice period, but given the asymmetry of employer-employee power, that ends up being pretty common. For at-will employment, I don’t think there needs to be any severance package or mandatory weeks of pay, but I think it’s offered in many cases.
Having said that, in finance (I used to work at a proprietary trading firm in an at-will state), it’s extremely common for firings to be immediate, e.g., arrive at work, boss calls you to office, get fired, badge taken and you’re walked out and your desk belongings are mailed to you later. More often, you’re walked to your desk to pick up your things instead of having them mailed out, but both happen. But even more often, people are “incentivized” through bad reviews and bad bonuses to quit in advance of a firing.
When I quit, they didn’t want me to leave, and I negotiated a couple weeks of notice to hand over my responsibilities and knowledge, and to maintain some relationships.
I had a non-compete in my original contract, so I would have to negotiate with the original firm as to whether they would enforce it. If so, I would receive gardening leave pay in order to delay my employment at a competing firm. That could be for as much as 2 years, and they would pay my base salary at the original firm in order for me to not start at the competition. This gardening leave is totally different than a severance package though.