The £351.4m figure quoted isn't even the full extent of their debts.
In total they owe a staggering £472 million, which breaks down as follows;
£233m owed to RBS
£144m owed to Hicks and Gilette*
£35m owed in transfers
£14m owed in taxes
They have also received money in advance for season ticket sales, sponsorship deals, and so on, which amounts to £28 million, and goes down as a liability since they have yet to provide the service/whatever.
And there are a further £16m of expenses for which they are still awaiting billing.
* This was former bank debt, which was very likely borrowed by Hicks and Gilette in America for 6-8% interest, put through their "company" in the Cayman Islands and then loaned to Liverpool, at 10% interest. Currently, that debt is with the holding company, but it will be transferred to the club if and when it is sold. There is some chance that this debt was written off in the few months after these accounts closed (the club announced that it was, but there is a very good chance that some "creative accounting" means this isn't really true), but that won't be clear until next year's figures.