You are searching for the false-negative rate of these tests. A test resulting in a negative outcome while it should have been a positive outcome.
A recent article stated that most of the false-negatives of COVID-19 tests are actually caused by not properly taking the samples from nose and throat. While I cannot find the original article I've got this information from, I've added two other relevant quotes. So yes false-negatives are possible but are likely caused by samples that are not properly collected.
The rollout of COVID-19 testing is accelerating as more kits become available. However, a leading pathologist who was director of virology at Stanford, points out that the results are not 100% accurate. "It's not that these tests can't detect virus," said Dr. Bruce Patterson. "My concern is that the sampling involved in detecting the virus can lead to clinical false negatives." - https://abc7news.com/6053940/
Also, the false-negative rate can vary based on the test method used and its quality and accuracy.
COVID-19 tests are new, and assessing their accuracy is challenging. PCR tests may produce false negatives, failing to identify evidence of SARS-CoV-2. Sometimes false negatives result from human error or problems with the procedure. Giving the test too early or late, for example, can lead to a false negative. - https://www.medicalnewstoday.com/articles/coronavirus-testing#accuracy