If I take a DNA test, can it expose a relative I have never met?
Yes. Because you share DNA with relatives, your test can make a relative partially identifiable through you, even if they never tested themselves.
This is one of the genuinely unsettling implications of consumer genetic testing, and it is no longer hypothetical. The well-known example is the Golden State Killer case, where investigators uploaded crime-scene DNA to a public ancestry database, identified distant relatives, and used traditional genealogy to narrow down the individual. Nobody in that chain had to test the suspect directly.
The implication for ordinary people: you do not have to take a test for your DNA to be partly searchable. If a cousin you have never met tests and uploads to a public database, some of your own genetic information becomes inferable through them. For most people with no criminal exposure the practical risk is small, but the privacy principle is real, and it is one reason to read a company's data-sharing and law-enforcement policy before uploading anywhere.
And it is why consent is not purely individual with genetic data. When you test, you are making a small decision on behalf of parents, siblings, and children who share your DNA. That is not a reason to avoid testing, but it is a reason to choose a provider with clear, restrictive data policies and to think of the choice as a family one.