Sorry if that wasn’t clear. The PCR test is a viral test, to see, if you have a virus in your body. People who are tested between getting infected and some time after having an immune response, will come back positve. I am not sure for how long after an immune response, but possibly weeks after they still have the mentioned viral debris in their body (i.e. left-over bits of the destroyed virus). But over time that viral debris does get removed from the body and then people come back negative.
The viral test is not the same as an antibody test. Antibodies are proteins that are built after you had an infection of a specific disease. They remain in your body and that’s what causes immunity to a certain disease. So the antibody tests look for those proteins, not for the virus, they look for immunity, rather than infection.
So in conclusion, if you’ve had a Sars-Cov-2 infection, after some time the PCR viral test should come back negative, but the antibody test should always come back positive. I hope this makes sense.