If a tachyon starts from where you are and goes away at faster than the speed of light, you will see the photons it emits earlier than it actually departs.
So you will see all these photons coming as if the tachyon were coming toward you at a speed slower than light, and then bang, the tachyon leaves.
In fact, the faster it is going away, the slower it appears to be arriving.
EDIT: You can just tell this from a space-time diagram:
T s C
| / /
|/ / f
| s / /
|/ / f /
| / / /
|/__/_/___X
| / /
| / /
|/ /
| /
|/
Here, the time T axis is vertical and the space X axis is horizontal.
Line C represents the speed of light. Photons move parallel to that line.
If something is moving away from you slower than light, it is a diagonal line falling in the slow (s) region. When it emits photons, they travel parallel to C, so each one arrives back at you at a later time.
That's the normal behavior that you're used to.
If something is moving away from you faster than light, it is a diagonal line in the fast (f) region. When it emits photons, they travel parallel to C, and thus arrive back to you at a negative time, relative to when the object left you.
In fact the faster it's moving (closer to horizontal) the earlier its photons will arrive (negative T).
The slower it's moving (closer to C) the more its photons will appear to come all at once, just before it "departs".
Yes, if a particle would be travelling faster than light, it would always travel faster than light. This is what's called a tachyon, and they have in some sense imaginary mass.
The three regimes, time-like, light-like and space-like (i.e. subluminal, luminal and superluminal space-time distances) are invariant under Lorentz transformation. Therefore anything on a super-luminal 'mass-shell' would always stay there and could not be decelerated to light/ or sub-light speed.
The problem is not that it would violate relativity, but rather causality, since with faster than light information propagation one could 'travel back in time', therefore leading to paradoxes.
For an introduction check out Wikipedia
Best Answer
As a matter of fact, Einstein's theory of relativity is what predicts the possibility of tachyons (faster-than-light particles) - or rather, relativity is what makes tachyons special. Without relativity, particles moving faster than light would just be really fast particles.
Although it's often said that Einstein's relativity says that nothing can move faster than light, that's not actually true. What special relativity actually says (among many other things) is that anything which moves slower than light will always move slower than light, anything which moves at the speed of light will always move at the speed of light, and anything which moves faster than light will always move faster than light. Effectively, nothing can cross the "barrier" of light speed. So there is nothing in relativity that forbids the existence of tachyons.
However, based on relativity and other theories, we can predict certain properties that tachyons would have, if they exist, and they turn out to be rather strange. For example, their mass would have to be represented by an imaginary number. Also, a tachyon would get faster and faster as it loses energy, as opposed to normal particles, which need to gain energy to increase their speed. If you follow this sort of reasoning far enough, eventually you wind up with nonsensical results. Combined with the fact that no sign of a real tachyon has never been observed, this leads most physicists to believe that tachyons either do not exist, or are prohibited (by some as-yet-unknown law of physics) from interacting with normal matter.
If you're interested in learning more, I would second the suggestion that you check out the Wikipedia article that anna linked to in a comment.