Usually it depends on the IC explanation (if any) for disappearance (death, travelling, etc.) but generally, if it is known that the player is not coming back anytime soon, the items go to the land of "the lost and the found", typically by those in the vicinity of the disappearing character's last known location. Sometimes, the gone character is CC'ed into granting the items if such a will can be claimed to have been made.
If the player just disappears without a trace (as in, logged in one day, didn't log in mysteriously for some time afterwards) then the items, by the nature of the claims list, immediately go back onto the market, but do not tend to change hands until someone claims the item for himself/herself and successfully backs up the claim, either with a logical appeal or with the aforementioned "lost and found" method.
You can claim whatever you want, but people don't tend to accept that you claim some missing person's stuff unless they have been MIA for at least a few weeks. However, that doesn't mean you can't start claiming stuff from day 1, just that you have to one way or another deal with those who challenge the claim, either wanting the item(s) for themselves or simply wanting to stand up for the absent party.