"distressing example" is correct and usable in written English.
You can use it when you are trying to describe a situation that is upsetting or disheartening. For example, "The homeless man's story was a distressing example of the struggles many face in our society today."
People with HIV are a particularly distressing example.
One distressing example is the administration's sneaky effort to reverse a Clinton rule phasing out snowmobiles from Yellowstone National Park -- a rule buttressed by overwhelming public approval and years of conscientious science.
This is a distressing example by our nation's finest medical centers of the shameful practice of placing financial concerns before the needs of the patients that they claim to serve.
The minister for mental health, Alistair Burt, who has called for more research after previously admitting his department does not know the number of child deaths in mental health units, said: "This is another distressing example of inadequate care in a mental health setting and I offer my sincere condolences to Ms El-Keria's family.
Yahoo is a distressing example of the former error–hell-bent optimism.
A distressing example is his proposal to slash $3 billion from the Low Income Home Energy Assistance Program, which provides cash assistance to poor people to help them pay their utility bills.
Some reports contain distressing examples of behaviour by traumatised children.
When I left Port-au-Prince, after 18 days of witnessing the most distressing and inspiring examples of the human condition I had ever seen, I knew I'd return one day, I just didn't think it would be so soon.
Before they left England, he had warned them not to celebrate too exuberantly, lest they set a poor example during a distressing economic time.
Finally, some interviewees discussed matters that were distressing for the researcher, for example violence (as perpetrators or survivors).
On the one hand, it is argued that euthanasia might contribute to a good, dignified, "civilized" death, for example by preventing distressing forms of suicide.
