Most data collectors (assuming you're using a robotic gun) allow the field surveyor to automatically do that. For example, they can take a shot 3' closer to the gun, and key in the fact that their target is 3' behind them. Or they can shoot off to the side, and say "I shot 3' off to the the side". Data collectors like the Trimble TSC3 have built-in compasses and GPS, so they can actually just stand at the point they shoot, point the data collector at the target, and key in "It's 3' away, in the direction I'm pointing my data collector".
With older systems, it get's more laborious. If you're importing through the Survey Database, then one way is to unlock the point in the Survey Database, and move it manually. This assumes, of course, that you don't expect to simply import Survey Database information into any newly-created drawing and have it be correct. But I've found no value in that approach, in any case. So I don't reallly view that as much of a down-side, although I've heard of some companies who expect to work that way. But I personally think they are making a mistake.