The phrase "a depressing example" is correct and usable in written English.
It can be used when referring to an instance or case that evokes feelings of sadness or hopelessness.
Example: "The report presented a depressing example of the impact of climate change on local communities."
Alternatives: "a disheartening case" or "a bleak illustration".
For decades, the state of Bihar was considered a depressing example of the failure of large parts of India to move forward and tackle poverty.
The discussion of the committee'sreport (pdf) on the economics of immigration is a depressing example of what's wrong with the debate on immigration in Britain.
In that context, it is a depressing example of the inability of the Super League clubs to see the bigger picture that none of them has identified Scotland as a target area.
In a country suffering weak productivity, low skills, ineffectual unions and stagnant living standards, the road haulage industry offers a depressing example of industrial inertia meeting the anti-intervention dogma of government.
For a depressing example of how members of Congress can be spoon-fed the views and even the exact words of high-powered lobbying firms, consider remarks inserted into the Congressional Record after the debate and vote on health care reform in the House.
If anything, Jihadi John is but a depressing example of the banality of evil.
Today, it's a particularly depressing example of paradise lost.
There is no doubt that, for many office workers in the Javits Building (itself an unusually depressing example of government architecture), "Tilted Arc" was an eyesore, a menacing, intimidating barrier whose tilt made some pedestrians feel it was about to fall on them.
When Democratic Senators failed to stop Republicans from filibustering the DISCLOSE Act last Tuesday, it was an especially depressing example of the party's weakness.
But, more likely, this is just an extremely depressing example of how much someone is willing to humiliate themselves to remain famous for another week.
