If you are a criminal suspect, fugitive or have an outstanding warrant, the worst thing you can do is get on an airplane where you're on a ticket in your own name.
I've been on a couple of flights this decade where marshals have been escorting a shackled prisoner. At ELP, I was on the first flight out to ATL in the morning and, when I got to the gate, the pilots, flight attendants and all the other passengers were waiting at the gate with the boarding door closed. About 5 minutes later, from the opposite end of the concourse from security, two marshals are escorting a prisoner in a blue jumpsuit. On cue, the GA opened the door and the threesome went immediately on board, bound for the last row; the pilots and FAs followed, and then boarding started a few minutes later. When we got to ATL, the threesome deplaned via the emergency stairs in the back of the MD-88; the paddywagon was waiting for them on the tarmac.
When I did the "Walk a Mile" with the ATL gate agents in October, 2010, one of our passengers was an FBI agent who was packing heat (the GAs were alerted as to who he was and he was allowed to board first). When I saw your title "Federal Agents", I was thinking of that gentleman.