That's going to vary quite a bit by job and country. Possibly even state. And have a certain amount to do with what you get from your employer.
For example, I'd expect that a confirmation letter would include:
- a formal recognition of your last day of work at the company
- a formal recognition of what or when your final paycheck will be
- declaration of any health insurance coverage termination (or other benefits)
- the policy for closure of any time off related benefits (for example, in some companies, floating holidays are not reimbursed, but accrued vacation time is, and will be included in a final pay check)
- formal notification of anything of significant value that they are expecting you to return before you leave (laptops, proprietary data, licensed software, etc.)
- formal notification of the termination of anything specific to your situation (for example, if you carry a security clearance, there's steps that have to get covered when you leave. Similarly - NDAs, and non-compete agreements)
- a notification of any and all final steps you are expected to take as a terminating employee
- a notice that you should resolve any debts on corporate accounts for which you are responsible and hand in all credit attached to the company (ie, a corporate card - don't leave a bill to be paid after you leave)
- formal clarification of any cases where you have been a legal representative of the company in some way, or where the lines between you the individual and the company are blurred (credit accounts, pending bills, speaking on IP related topics, etc.)
That's a pretty long list, and there's no formula I know of for what part of this laundry list gets covered in a formal closure letter, vs. your boss just coming to you and saying 'hey do this...' Usually, the more likely it is to have previously involved a lawsuit, the more likely it is to be in a formal letter drafted by lawyers.
There's also stuff that comes up like surveys that may come in such a letter.
I know of no case where lack of a formal letter left you in a legal bind (caveat: I'm not a lawyer). For the most part, these notifications cover the company more than the worker. In terms of unemployment and other worker benefits, the legal coverage is the offer letter, not the termination letter of the previous employer.
But the legal side of it is that if there is something you should understand very clearly, then you have the right to be told about it, clearly, in writing, in a timely manner.
A few days vs. a few weeks
If you work in a big a company, your manager has almost no hope of predicting when the letter will arrive. So do not stress out about having heard the letter would arrive "in a few days" vs. the letter arriving in 7-10 days. If you are within 3-5 days of your last day at work, and you haven't gotten it - tell your manager. But don't worry if 3 days becomes 5. The wheels of Management->HR->formal letter writing are never the quickest process in a big organization, and this is usually pretty low on the queue of things to do for a big company.
I'm freaking out, because I don't have a letter
There is very likely an HR manual on employment policies. Read up on your company's termination policy. This is as legally binding and as clear cut as the letter you are likely to receive. Check that guideline and if it doesn't cover an issue listed above, talk to your manager.
What's ironic is that while dealing with the closure of employees' last days at a company is very much the responsibility of middle management, it's quite typical that middle management will have absolutely no clue about:
- the contents of these letters
- when they will arrive
- how they are sent
Having not (yet) quit the company, it's quite likely that your manager has not seen the letter. So it's usually best to go at the problem as a conversation with your manager on what he knows your legal obligations and responsibilities to be. At the very least, you'll have his take on it, and it'll help round out any gaps that you might leave behind.