I went through one of these projects. The tech debt was never as bad as you describe, but it was a small company operating on a short runway. It also taught me an unfortunate lesson about non-technical founders and the dangers of outsourced code.
The MVP for the company had been bought off the shelf. It worked fine, but the code was abstruse and utterly resistant to change. As the price (in time and dollars) of change requests grew, they sensibly in-housed development. Unfortunately, their clients had some idea what to expect in terms of features per day and dollar. Requests like "let us use our logo and custom color scheme" turned out to be serious challenges since every color and style decision was clumsily hardcoded, so we took far too long to achieve them.
Ultimately, we ended up a contract behind - bringing in business to fund delivering on the previous request. Most startups operate under the gun like that (with either fundraising or contracts), but they start there and labor to escape. We started solvent, and had no clear plan to break out of tech debt - a rebuild would have been too slow, 'working smarter' wasn't viable, and expanding the tech team would have come too late and too costly.
So, we died. Not because we couldn't do work, but because we couldn't do it at a competitive speed.