My previous employer failed after almost ten years of venture funding (mostly because it is pretty hard to make a good return on ten years of investment). We had a lot of technical debt. It did not kill us, per se, although I think it was correlated with problems in the company: a lot of things would have been easily resolved had we been less pressed for engineering time. We never had enough revenue to grow the engineering team significantly, and what engineers were there were often fire-fighting. There may have been indirect causal effects like causing good people to get frustrated and leave, or simply causing good people to get frustrated and avoid working on certain problems. We had a few people who flipped out and started repaying the principal (including myself), but they were taking limited engineering time from things that the company needed day-to-day.

It may be true that technical debt directly kills some products, but if it's bad enough that you can't get certain things done, even if what you do instead is also important to the business, the debt is a sign of bad engineering management (either in the past or the present). And bad engineering management will kill the product.