The ship came back to Earth in half. Why didn't the Arbiter tell them that the portal closed as the ship was going through?
The Arbiter didn't need to tell anyone the hole collapsed. It was a few kilometers above the surface of the Earth. Everyone saw it collapse when the Arbiter returned. It wasn't a secret.
Maybe then they could initiate a search campaign wherever the portal was for the other half to try and retrieve MC's remains (shock, horror to them that he's just asleep!)?
On the other end of the portal was a firing Halo located somewhere outside the galaxy's rim, substantially further than anyone on Earth had ever traveled. If they did spend the money and time to do a search, they could spend hundreds of decades and turn up with nothing because of the Halo weapon's blast. It wouldn't make sense to conduct any searches at all. As far as they know, the Chief died amid the blast of the Halo when the ship was severed as the portal collapsed.
Is the Arbiter really just that much of a dick that he didn't want to tell them so MC was stuck out there all this time? Maybe he wants MC out of the way so he can wipe-out the human race without their saviour getting in his way?
The Arbiter believes the Chief to be dead as does the rest of humanity. The Chief didn't die, however, but the portal sent him somewhere else, presumably inside our galaxy. The Halo ring's firing couldn't be sustained and blew apart, destroying the Ark and itself, wiping out the Flood. At the very end of the game, beyond the cinematic showing the Chief's survival, is a brief one (only appearing on Legendary) which shows the severed ship with the Chief aboard is heading to some sort of populated world with faint architecture that appeared Forerunner.
