"Essential" services are kept running. Throwing people in prison for selling drugs is essential, as it turns out, as is making press releases about it.
The government still exists, but there's no legal authority for many (but not all) of the federal employees to do work for the government, since there is no appropriation in force to pay for that work.
Those who are working are essentially working for the promise of payment at some indefinite time in the future (except for the military, who apparently really are a sacred cow...).
Government employee here. Many of us aren't working on the promise of payment - we've already been paid. My salary was already "paid" two years ago. Congress passed a bill, the president signed it, and the DOE gave us the money. Now, if the government shutdown lasts until May, we'll probably be out of that money then I'd stop receiving paychecks. Of course, I hope to have a new job by that point, anyway.
Are you a government employee, or a contractor? I know that there are some persons paid for by multi-year appropriation bills, but those are comparatively rare. Most expenditures are handled via a single-FY appropriation (and my understanding is that this covers all APF employees).
If you're a contractor, on the other hand, then you're not a government employee (legally), so the whole discussion doesn't apply to you directly.
Government shutdowns are done in a way that retains a certain subset of services that are either paid for through unaffected funding mechanisms, or have been designated essential. That includes soldiers' salaries, payments to military contractors, operations of the FBI and DEA, and small to medium-sized portions of other agencies (e.g. the EPA is mostly shut down, but the Superfund and Mine Safety divisions will stay open).
