Is it possible to cough up a cancerous lung tumor without noticing it?

[derekt1919]

About a month ago, my mother had surgery to remove a high-grade neuroendocrine tumor from her brain.  It was hypothesized that it spread there from her lung because a previous CT scan showed a 3cm tumor on her right lung.  Pulmonologists performed a bronchoscopy to sample the tumor and send it for a biopsy.  But they reported to her the next day that they were unable to find the tumor.  They sampled a lymph node instead.  My mother believes that she may have just coughed it up, but she doesn't remember coughing up anything significant.  Is this possible?  If not, what may have happened?  She has no symptoms of lung cancer aside from an occasional dry cough and slight clubbing in her fingernails, which seems to be going down on its own.  I am completely perplexed and have no idea what to think.