If you look closely at US startups you'll usually find the founders and senior staff are on "notice required" contracts of several months.
- You can do it in mutual agreement (see below).
- You can quit directly but you generally forgo any company benefits (like build up bonuses) and you might/most likely not have rights to state-supported unemployment benefits (70% of your last paycheck).
As an employer:
- You can either in mutual agreement (in which case the employee usually also keeps his/her rights since the contract does not end abruptly).
- By court order but this usually requires extensive documentation on malpractice of the employee.
Notice time usually is at least 1 full month in most cases, can be shorter if the employment is not time-fixed or by agreement. All notices are for both employer and employee.
I do not know exactly but if you have build up "vacation days" you usually cannot use those in your last month and forgo those, unless you agree with your employer in some sort of scheme. "Going in sick" will get you reported in which case a investigator will check you out and you most likely will forgo your sickness benefits. (I've had this once already, but not for contract finalization but reporting it really late. The guy was very surprised to see someone actually sick when he checked it out so I guess abuse happens often.)
There are some contract termination clauses (money mostly) in some contracts I've seen but as far as I know they are not enforceable in any way (since that equals servitude by power). Thinks like immediately handing back lease-cars and laptops under force of fine are though.
Yes, but at least California courts have found these "garden leave" provisions in contracts are not enforceable. 
As for the rest of the United States, I'm not sure, but it seems like somewhat unsettled law as such notice requirements are quite rare in the US.
1. " And it turns out that companies also cannot require their employees to provide any specific length of notice, even when they offer to compensate them at 100% of their salary and benefits for the duration of the notice period. California courts have found these mandatory provisions to be an unenforceable restraint, as well." https://www.huffingtonpost.com/entry/understanding-californi...
Modern slavery is things like confiscating the passports of your immigrant workers so they can't escape.