Fry and Leela join Planet Express as replacements. What happened to the old Planet Express crew?
As written at the end of Space Pilot 3000, it was a space wasp that led to the demise of the crew that Fry, Leela & Bender replaced. It became bees later in "The Sting", as already mentioned.
The wasp presumably ate them, as opposed to the bees, which were simply trying to sting them to death in a manner where their "eyes boiled out like science fair volcanoes" (AFAIR).
There is the professor holding the envelope with the career chips.
Actually there are multiple lost space crews. Not only the crew from the episode Space Pilot 3000 but from the episode with the giant multi dimensional space whale. The whole space whale episode was dedicated to finding the truth about what happened to the first ever Planet Express delivery crew. The episode Space Pilot 3000 crew were actually just replacements themselves for the crew that was eaten by a giant multi dimensional space whale.
The pilot episode reveals that the crew before them were eaten by Space Wasps. When Leela points out that they still need carrer chips (I know. What are those, right.), the professor pulls out a bag labeled 'Contents from Space Wasp's Stomach'. Yet in 'The Sting', the professor says that the crew died while gathering space honey from space bees, making a liar out of the pilot.
Yet in one of the more recent episodes, the current crew were revealed to be lost while trying to kill a Moby Dick like space whale, thus making liars of the previous two episodes about the previous crew.
Therefore, I have come to the conclusion that there are more than one previous crew and I feel that we will see more fates of other crews.