Fire Fighter/Fire Speculator
Crassus was by far the richest man in Rome during his day. The way he amassed his fortune was by offering insurance to people who's houses were burning down, in exchange for helping to put it out (well, having his slaves help put it out). Moreover, he would buy burned down and damaged houses in prime real estate areas, rebuild them, and sell them for massive profit. Rome was constantly burning back then, so this was big business (the folks you send back can obviously maintain only a small-time operation to remain under the radar).
The limitation here is that it requires that the person you're sending back bring startup capital to acquire skilled construction slaves and burned lots in the first place. Still, it's probably one of the more safe/relaxing jobs out there, and has big money making potential if they want to enjoy a comfortable existence.
Edit: That said, as LSerni points out, the big fish could very easily go after you to beat you up and shut down your operation. You would definetly need to either have mafia connections (the mafia or "collegia" were a big deal), or you could kick some profits back to crassus, in exchange for him not going after you.
Here's a case where they can cheat the system a bit. Roman soldiers were paid quite poorly, but they'd let anybody join up as long as you could hold your own in a fight. In the course of normal campaigns it would certainly not be worth it to tag along, but soldiers were also paid in the loot they acquired. Since your travelers know all the campaigns (and will be trying not to alter them), they will know when to tag along for safe/easy loot, and which campaigns to avoid. Not only that, they know exactly where to go during battles/sieges for the most looting potential.