According to one account of the meeting, the government begged Mr Alimucaj for money to help avert an economic and political catastrophe. Mr Alimucaj, in turn, begged the government for money to bail out his own high-interest investment scheme - by far the most popular in the country - before it, too, goes belly-up. As one diplomatic source commented: "It was as if two friends had gone out for dinner and then realised they had both lost their wallets."
With hundreds of thousands of Albanians facing the loss of their life savings, not to mention their houses, cars, cattle and other valuables that have been hocked along the way, the country is awhirl with crazy stories of cabinet ministers' wives frantically withdrawing their cash the night before one scheme collapsed, of a speedboat suddenly leaving the port of Vlora for Italy with $130,000 on board, or of the secretary of one failed scheme running out of the office with $50,000 in fresh banknotes stuffed into a suitcase.
How did Albania tumble to the brink of anarchy and social collapse simply because of a handful of financial scams? After all, pyramid schemes - unregulated pseudo-banks which use the deposits of one lot of savers to pay out implausibly high interest rates to a second lot, attracting an ever-widening circle of investors before vanishing overnight and absconding with the accumulated booty - have come and gone all over Eastern Europe. They have always stirred up misery and anger, but never have they threatened the stability of an entire country.
The truth is, Albania is a rather special case. In most countries, schemes lasted little more than six months, but here some have been going for years. Whole swathes of society unable to survive on meagre state wages and pensions have come to rely on them - an investment of $3000 (pounds 1850), for example, providing a perfectly respectable income of around $250 (pounds 154) a month.
This seems to defy economic logic, until one considers a possibility, widely acknowledged and confirmed by those in the know, that the longer- lasting pyramid schemes were also businesses for the laundering of dirty money.
According to Western intelligence agents, Albania has raked in money from the illegal sale and transport of oil to Serbia and Montenegro, from the transport of arms and drugs, and from various rackets including the prostitution of Albanians in Italy.
Albania is believed to have become a haven for dirty money from elsewhere in the world, largely because the commissioned charged for laundering is significantly lower than in Switzerland or other traditional centres.
The hypothesis is that Albania's ruling Democratic Party used the schemes both as a money-recycling operation and, with the high interest payments, as a way of buying political support from the people. For a long time the interest rates remained stable at 6-8 per cent per month, and the system seemed to chug along nicely. It was not true, therefore, that ordinary Albanians were duped by the schemes; rather, they understood how they worked and believed they would continue because a collapse would mean the destruction of the entire ruling order.
The schemes began to cause international concern more than a year ago, and some members of the government and the governor of the national bank lobbied unsuccessfully for them to be shut down.
Then something began to go wrong. During the summer the various schemes began an interest-rate war which made the payments more and more unrealistic - up to 100 per cent per month. Perhaps the sheer weight of investors forced some schemes to up their interest rates as a way of attracting new capital.
Another theory, offered by a prominent Albanian with links to both the government and banks, was that one source of dirty money was switched off - namely the profits from the illegal sale of Iraqi oil that were being laundered, he alleged, by the first big scheme to go under - which was run by a gypsy woman called Sudje.
In order to stay afloat, the source said, Sudje had to turn into a pyramid by default, her interest rate rises sucked capital away from the other schemes and the ensuing rates war led to the present crisis.
Still the government did not act, partly because it had a local election campaign to fight in October in which the ruling party's main slogan, printed on posters overtly sponsored by the finance companies, was: "Vote Democrat and everybody profits."
It did not take long for the rot to set in. The schemes, which had previously accepted any currency, began restricting deposits to Italian lire, or in the case of Xhaferri and Populli, the schemes that went under most recently, to Albanian lek.
It was the risk of the market being flooded with billions of lek, a sure recipe for severe inflation, that pushed the government into action - with some stern prompting from the International Monetary Fund which sent a delegation in November to try to negotiate a package of limited credit for this year. The negotiations are now on hold, a factor which will almost certainly keep the heavyweight investors out of Albania for the time being.
Xhaferri and Populli were closed down last week, just before they were supposed to pay out three months' interest, and their funds - estimated by the government at around $255m (pounds 157m) - frozen. A third big fund from Vlora called Gjallica has promised to make payments that are already overdue next Wednesday, but it too has almost certainly gone bust and its assets - some $300m (pounds 185m) according to some estimates - frozen by the government.
That leaves the big heavyweights - Mr Alimucaj's company Vefa, Kamberri of Vlora and Silva of Tirana - out in the field, but for how long nobody knows. Vefa, which runs supermarkets, chicken farms, hotels and other interests, has become closely identified with the government. Its collapse would be catastrophic, economically and politically.
President Sali Berisha, asked about Vefa at a news conference, failed to vouch for its creditworthiness and said government auditors were checking its books - an ominous signal. Some political sources say he is anxious for Vefa survive at least until next month, when he is up for re-election via a vote in parliament.
Deep cracks are appearing, though, in the Democratic Party structure, with tension particularly high between Mr Berisha and his prime minister, Aleksander Meksi.
The Albanian people now find themselves staring into an abyss. Not only have they lost their savings, but the most significant part of their income, too. If they stop spending, shops and small businesses will start failing and the whole system will come crashing down. Last weekend, the closure of Xhaferri and Populli led to riots that destroyed city council buildings, courthouses and police stations across the country. If Vefa and the other companies blow too, as informed opinion believes they must, the popular reaction may be nothing short of terrifying.