Research has been showing that if you test positive for the virus, you will continue to come up positive on later tests for at least 90 days even though you are not able to transmit it to others after days 10 - 14. This is according to what USAF doctors told my sister-in-law.
Depends on the test used, I think. The saliva tests are less likely to pop positive thanks to viral debris than the nasal swabs.