DigFinex is the majority owner of Tether Holdings Limited and IFinex Inc, and operates as the ultimate parent company of Bitfinex and Tether.
Tethers are cryptographic tokens which claim to be backed 1 for 1 with US dollars held in bank accounts. Tethers are the most popular cryptocurrency in the world by turnover, recently exceeding Bitcoin in turnover value, despite having a vastly smaller market capitalisation.
The lawsuit alleges that Bitfinex had created and been in control of Tether Holdings Limited since September 2014 and that the same individuals in control of Bitfinex were also secretly in control of Tether, noting that the overlapping control structure between Tether and Bitfinex had been largely concealed from the public until it was revealed by the Paradise Papers leak in November 2017.
The lawsuit alleges that initially, USDT was only transferred from Tether’s “treasury wallet” to Bitfinex, and not to any other exchanges. The lawsuit states at  that:
Tether’s treasury wallet is the account solely controlled by Tether in which all USDT are created or destroyed. All new USDT are first sent to the Tether Treasury after being created. Any redeemed USDT must similarly be transferred back to the Treasury to be “revoked,” i.e. destroy.
The lawsuit claims that the leveraging of USDT by Bitfinex and Tether is the primary cause of the inflation, and subsequent deflation of the 2017-18 Bitcoin Bubble, claiming that the creation and loss of $265 billion in Bitcoin value was the result of Bitfinex and Tether propping and popping a massive asset bubble (possibly one of the largest bubbles in history). If true, it's somewhat impressive that Bitcoin is even still around with such dramatic interference in what is supposed to be an extremely free market.
The combined market capitalization of all digital currencies as of January 6, 2018 was roughly $795 billion, and the total value had dropped to $329 billion by February 2018. The lawsuit claimed that in response to this significant drop in prices, Bitfinex and Tether issued billions of unbacked USDT to manipulate the price of Bitcoin, enabling Bitfinex and Tether to buy massive amounts of Bitcoin without paying for them(which is very similar to allegations brought against Mr Karpeles in the Mt Gox case in 2013-2014) and then selling them for US dollars.
The lawsuit substantiated this by stating at  that:
If anyone ever asks questions, Tether can convert cryptocurrencies to U.S. dollars or use its U.S. dollar profits to retroactively provide reserves for USDT and claim those reserves were there all along.
This alleged manipulation would mean that Tether and Bitfinex engaged in what is known as a "pump and dump" scheme, which would basically involve the following:
Bitfinex buying Bitcoin (or options to buy Bitcoin);
Bitfinex minting unbacked Tethers;
Bitfinex using unbacked Tethers (still trading for $1 USD each) to bid to buy Bitcoin;
After the price of Bitcoin has increased, due to Bitfinex buying Bitcoin in Step 3, the sale of the Bitcoin (or options);
The use of the profits of the sale in Step 4 to buy back the unbacked Tethers, which would then be burned.
The plaintiffs’ claim monetary damages as a result of the manipulation and true to US lawsuit style and penalty damages, are seeking over a trillion dollars in damages (or $400 billion more than all of the assets currently under management at Goldman Sachs and vastly more than Bitfinex has in assets).
Allegations that Tether has been used to manipulate the cryptocurrency market have circulated for more than a year. In a study published last June, researchers with the University of Texas at Austin said bitcoin’s price rose after Tether was used by the Bitfinex exchange to purchase bitcoin when prices were falling. A long running Twitter account @Bitfinex'ed details ongoing claims against Bitfinex and Tether.
In what would seem like an anticipatory act, envisaging the imminent lawsuit, Bitfinex published an article on its blog on October 5, 2019, stating that it:
is aware of an unpublished and non-peer reviewed paper falsely positing that Tether issuances are responsible for manipulating the cryptocurrency market.
The sheer scale of the lawsuit, coupled with the challenges Tether has faced (including having to rely on a law firm as an "audit" after being unable to pass an audit with an accounting firm, which is concerning and embarrassing) as well as Bitfinex having US$850 million in assets frozen earlier this year makes this one to watch.
Thanks to Petros Xenos for his assistance with this piece.