The following ruling was received from Hasbro, publisher of Monopoly and organiser of International Monopoly Tournaments. I have therefore completely rewritten this answer.
My questions to Hasbro :
The rules of Monopoly state that when a players goes bankrupt to the
bank, the player turns all assets over to the Bank. The Bank then
auctions off these properties.
Are all of the properties auctioned off at once as a single lot?
If they are auctioned one at a time, in what order are they auctioned? By value or randomly selected?
Hasbro agent's answers:
1. Are all of the properties auctioned off at once as a single lot?
No. All properties should be auctioned off one at a time.
2. If they are auctioned one at a time, in what order are they auctioned?
By value or randomly selected?
No specific order needed . The banker can randomly select. I have
also included the proper way to hold a Monopoly Auction just in case
it's needed. There is nothing terribly special with the process of
holding the auction, just a few simple rules.
When a property comes up for auction, whether a player declines to
purchase or a player goes bankrupt, the banker holds the auction.
There is no minimal bid so the starting price will always be $1 and
the property will goes to the highest bidder and the price is binding.
So if a player bids more than they have they can unintentionally
bankrupt themselves during the auction.
The auctioned property cannot be mortgaged by the highest bidder in
order to complete the purchase.
Important Note: All players can participate in property auctions –
this includes the banker, any players who may be in jail, and the
person who originally declined to purchase the property in the first