Rarely but it is possible. There are a couple of possible actions, which can result in false negative result in both urine and pregnancy blood tests.
If you believe you're pregnant and are using a urine pregnancy test, try diluting the sample, with distilled water, 10/1. If the result is still negative, you'll, likely, need to have an ultrasound done or wait for delivery, to be certain.
In the meantime, extremely high hcg levels or certain antibodies are indicative of increased likelihood of a false negative result, in pregnancy tests.
The 21ST century and "modern medicine" still can't determine whether or not a woman's pregnant; scary.