The March 1991 issue of Amazing Heroes (#189) has a notation in their release notations, saying that First had announced that they would no longer be publishing their superhero lines and were concentrating solely on The Classics Illustrated line. They did continue Lone Wolf & Cub, Beauty and the Beast, and Eric Shanower's Oz graphic novels.
Issue #197, August 1991, has a short piece about their financial trouble, as they seek $1.5 million in capital to pay off $600K in debt, owed to freelancers and others. They have ended their partnership with Berkley Books, on the Classics Illustrated line and are going it alone. Two of the titles within the line have been held up because of the money woes. It notes that Dark Horse has acquired Nexus and might pick up Badger.
#194 reports that Body Parts had been returned to creator Stephan Petrucha
#195, October 1991 notes that First has ceased soliciting titles and is still trying to see it's adventure titles. Several Classics Illustrated books are in limbo, at different stages...
The Comics Journal #142, June 1991, has a brief piece about First denying rumors of financial difficulties. The same article talks about Now comics avoiding liquidation, with a new buyer and Comico re-emerging, after sale to Andrew rev. All three companies were operating out of Chicago.
TCJ #143, July 1991 has a longer piece. Berkley had licensed the Classics Illustrated name and was in partnership with First. It wasn't panning out and they wanted to end, while First wanted to continue, so they went alone. They had also been working on a partnership with the Audubon Society, for a series of educational nature books. They dismissed half of their staff and were only publishing Classics Illustrated, Beauty & the Beast, and Lone Wolf and Cub, which were their bestsellers. BATB was tied to the Linda Hamilton and Ron Perlman tv series. 20 artists and writers working on Classics Illustrated had payments suspended and were owed between $1000 and 8000 each. Dark Horse bought Nexus and was interested in Badger. They were still looking for buyers for Sable, American Flagg, Grimjack, Dreadstar and Meta-4. They detail creators who are owed and for how much. Rick Obadiah says things are fine, that they are getting back on track and proceeding with plans for the Audobon books. Valerie Jones, a former editor, said she believed they were in deep debt and it was due to mismanagement and high overhead. Some of the Classics Illustrated people were talking about they believed they would be stiffed completely and others were exploring a class-action suit.
TCJ #144, Sep 1991 has an article about First and their refinancing plan, with an expansion on what was in Amazing Heroes, but covering the same ground.
TCJ #145, Oct 1991, has a brief note that First has suspended operations. Chief Operating Officer Patrick Morrissey, who made the re-financing announcement has been laid off and Rick Obadiah is operating with a skeleton staff.
TCJ #148, Feb 1992, notes that First Comics have closed their offices, in Chicago and their name was removed from the door. Rick Obadiah was working out of his home to sell off properties. The Audobon books never appeared and one of their last publications was The Classics Illustrated adaptation of Upton Sinclair's The Jungle. It notes their pioneering of using higher quality paper and higher prices (and profit margins) and peaked in the mid-80s. It mentions their hardboiled adventure series giving them an edge, until DC and Marvel started putting out similar material (which coincides with Mike Gold going back to DC).
Not much of an obituary; but it was TCJ.
As to why it wasn't as heavily publicized, Marvel went public, around that time, DC started the Impact line, the Image guys were making noises at Marvel, then left and comic shops in the US and Canada were being raided over adult materials, leading to the formation of the Comic Book Legal defense Fund. Dr Seuss passed away, as did Sheldon Mayer, Rick Griffin and Marvel's Direct Sales manager, Carol Kalish. They Journal wrote a scathing editorial attacking her, after running an obituary, which drew extensive wrath from Peter David (who had worked for her, before becoming a full-time writer) and several others. Kalish was a noted fan of comics, as well as a major force in building Marvel's Direct Market presence.
TCJ #149, March 1992 has a correction and that Obadiah was in a different office in the same building as the old production office. He was still trying to sell properties. howard Chaykin claimed First was in breach of their contract, since Flagg hadn't been published in over a year and that rights were due to revert to him, which Obadiah disputed.
A few issue later, stories emerge of artists complaining about problems at Eclipse.
In short succession, Now Comics, Comico and First went into bankruptcy or suspended operations, with brief revivals for the former 2. Eclipse soon followed , with rumblings in 1992 (and late books in 1991 that were due to cash flow problems), cat yronwode and Dean Mullaney's divorce, in 1993 (he had an affair and also tapped out a bank account) and pretty much ceased publishing in 1994 and went into bankruptcy liquidation in 1995, with Todd McFarlane buying up the lot. Well, except he never owned Miracleman, as it turned out.
Malibu was riding high on being the publishing partner for Image, but was done with that by 1994 and they had over extended themselves with Ultraverse and were in danger, then. They sold to Marvel in 1996, after DC initially showed interest. Kitchen Sink merged with Tundra, when Kevin Eastman bought in, then his stake was reduced and the company disappeared in the wake of the war between Diamond and Capital, after Marvel went self-distribution. Fantagraphics nearly went under in 1998, after Seven Hills book distributors went bankrupt, owing them a lot of money. They survived, thanks to appeals to the industry, which brought an influx of cash, by buying directly from them. Valiant ousted Shooter, was bought by Acclaim and was gone by the new Millennium. Marvel was bankrupt, by the end of the 90s, got bought up by Toy Biz, then, eventually, sold to Disney.
Dark Horse chugged along, with some ups and downs, but never to the point of danger.
Most of the influx of publishers, in the wake of the TMNT were gone in less than 5 years. Few of the publishers who started in the late 70s or early 80s survived the decade or the mid-90s. AC Comics continued, with its niche.