If you do not wish to buy the property, the Bank sells it at through an auction to the highest bidder. The high bidder pays the Bank the amount of the bid in cash and receives the Title Deed card for that property. Any player, including the one who declined the option to buy it at the printed price, may bid. Bidding may start at any price
So in this case the highest bidder is no one. As a result, no one will get the property.
EDIT: Actually, a better answer for how to interpret it -- all players passing is impossible, because if all but the last player passes, then the last player has won the auction (for $0) by virtue of everyone else having passed; they don't get to a chance to pass, because they win the auction before it'd ever be their turn to pass! This is actually a pretty natural intepretation and I think how some of the video game adaptations handle it.
May bid. No player is required to bid.
Assuming that, while the rules don't say so explicitly, what they really mean is that the last player in the circle is forced to take the property is unreasonable. That's a fairly complicated rules. If that's what they meant, they'd have said it, not left it up to the players to work out.
Sine they didn't say it, it's much more reasonable to think that they just assumed everyone knows how an auction works in real life. No one is forced to bid on a Picasso when it goes on the block. It doesn't get foisted on the last person on the bidding bench who makes no bid.
Besides, you can always immediately mortgage a property so it's always worth buying it for less than the mortgage price. The only situation I could imagine where everyone would pass is if everyone has exactly zero dollars, no houses and no unmortgaged properties, so nobody can afford to buy it for a dollar. In that extremely rare event, triggering bankruptcy of whoever landed on the property seems more reasonable to me than "nothing happens" because at least it advances the game.
That's what I'm saying. If the rules don't say what happens if everyone passes, assuming that no one gets the property is a very reasonable assumption. Assuming that we're requiring people to make $1 bids, or that the landing player has a "penalty," is an unreasonable assumption if the rules don't say that explicitly.
