They work the same way that the DNA-analysis machines work on CSI. You know the ones that you simply insert a slide of blood and you get an exact match in minutes? Which is to say that they work much, much, MUCH better on TV than they do in real life.
In theory, the serum would probably attempt to slow the metabolism of the person to incredibly slow levels...the heart would still beat, but just enough to keep brain cells from dying, or at least from dying too quickly. You probably wouldn’t fool a PET scan, but someone holding their finger to your neck might not detect a pulse. The antidote would return the metabolism to normal levels…’resurrecting’ the person, if you will. There are various animals that do similar things…hibernating squirrels, for example, are able to reduce their metabolisms to astoundingly low levels and recover with no apparent ill effects, so in theory, it should be doable.
However, people aren’t squirrels, and the likely outcome of administering a ‘fake death’ serum is very real death for the unfortunate recipient. We just don’t understand enough about how our bodies work to manipulate them on that level. We know that on very rare occasion, people who ‘die’ under very specific conditions (generally involving freezing water) can be brought back, often with side effects but sometimes seemingly none the worse for the wear. We also know that most of the time they simply die. I have no doubt that the CIA has cooked up something resembling the Alias serum, but I sure as hell wouldn’t want it used on me.