Below is what the Times said...sounds like the system is working as it's supposed to and the investigation needs to look into whether the serious adverse event (reportedly spinal inflammation) was vaccine related or not. Most vaccines have rare serious side effects (usually less than 1 in 1 million people), so if it's vaccine related, it could be an issue, but most of the time it's simple coincidence, as it's hard not to have a few out of 30K people in a trial not getting sick. In longer trials for chronic conditions (not vaccines usually, i.e., for things like diabetes or high blood pressure), there are often patients who die and those have to be closely compared for the treatment and the placebo groups.
https://www.nytimes.com/2020/09/08/health/coronavirus-astrazeneca-vaccine-safety.html
A person familiar with the situation, who spoke on the condition of anonymity, said that the participant who experienced the suspected adverse reaction had been enrolled in a Phase 2/3 trial based in the United Kingdom. The individual also said that a volunteer in the U.K. trial had received a diagnosis of transverse myelitis, an inflammatory syndrome that affects the spinal cord and is often sparked by viral infections. However, the timing of this diagnosis, and whether it was directly linked to AstraZeneca’s vaccine, is still unknown.
Transverse myelitis can result from a number of causes that set off the body’s inflammatory responses, including viral infections, said Dr. Gabriella Garcia, a neurologist at Yale New Haven Hospital. But, she added, the condition is often treatable with steroids.
AstraZeneca declined to comment on the location of the participant and did not confirm the diagnosis of transverse myelitis. “The event is being investigated by an independent committee, and it is too early to conclude the specific diagnosis,” the company said. Some said the company’s halt was evidence that the process was working as it should.
“At this stage, we don’t know if the events that triggered the hold are related to vaccination,” said Dr. Luciana Borio, who oversaw public health preparedness for the National Security Council under Mr. Trump and who was acting chief scientist at the F.D.A. under President Barack Obama. “But it is important for them to be thoroughly investigated.”
As an aside, most clinical trials of non-vaccines fail due to efficacy (57%) with only 17% failing due to safety (22% for commercial reasons). I haven't found similar data for vaccines, but I know from my work in the field that vaccines fail at an even lower rate for safety issues, although almost all vaccines have minor to moderate side effects (injection pain, mild fever, headaches, etc.), since they're affecting one's immune system on purpose and the body responds to the "invader" as it should.
This study assesses factors associated with regulatory approval or reasons for failure of investigational therapeutics in phase 3 or pivotal trials and rates of publication of trial results.
jamanetwork.com