Television today is full of shows themed around the unexplained. Ghost Hunters, Destination Truth, UFO Hunters, Mysteryquest, and Monsterquest and countless other series and specials. With all these shows out there though, one is bound to eventually come across what they are searching for, but that would then leave one big question: what would they do if they did find something?
Ghost shows probably wouldn't have to do much, most people will probably pass off any ghosts as tricks or CGI, except for the people who were actually there. What about physical things like crashed UFOs or a cryptid though? Most teams on TV from what I can tell aren't equipped to capture animals or bring back large pieces debris. There is also an inherent element of risk, especially with potentially dangerous cryptids like some of the ones Destination Truth goes after. All it takes is getting to close to a angry Sasquatch, and BAM! lights out for a crewman and most likely goodbye show.
Assuming that a team somehow does get the evidence of a lifetime, I'm pretty sure the producers of the show would have no problem handling the media bandwagon that would follow. After all, that is their primary job to begin with. The best part is that it probably wouldn't turn out like the Bigfoot costume in a freezer guys.