What happens to the food you accidentally aspire?
People can drown because of aspired food. If they don't then it can cause diseases, for example pneumonia. In extreme cases a tree can grow in the lungs. There are other aspiration/inhalation related diseases like silicosis or asbestos lung cancer. So it depends on the composition of the object (or liquid or powder) and other factors whether it causes a disease or not. I did not find anything about what exactly happens with these objects in the lungs. Probably the lung tries to get rid of them mechanically, if there is no success in that, then they cause a local inflammation, which can lead to diseases if it becomes chronic and/or the object contains pathogens.


  Common presenting symptoms (information available in 36 cases)
  included dyspnea (14), fever (9), and cough (6). A history of
  recurrent pneumonia was present in 9.



2007 - Pulmonary Disease due to Aspiration of Food and Other Particulate Matter: A Clinicopathologic Study of 59 Cases Diagnosed on Biopsy or Resection Specimens



  The annual overall inpatient cost associated with pediatric bronchial
  foreign-body aspiration is approximately $12.8 million. Combined, the
  rate of death or anoxic brain injury associated with pediatric foreign
  body is approximately 4%.



2014 - The national cost burden of bronchial foreign body aspiration in children



  Gastric aspiration is a high-risk condition for lung injury.
  Consequences range from subclinical pneumonitis to respiratory
  failure, with fibrosis development in some patients. Little is known
  about how the lung repairs aspiration-induced injury.



2015 -Resolution of Lung Injury after a Single Event of Aspiration : A Model of Bilateral Instillation of Whole Gastric Fluid



  Aspiration is a common but underrecognized clinicopathologic entity,
  with varied radiographic manifestations. Aspiration represents a
  spectrum of diseases, including diffuse aspiration bronchiolitis,
  aspiration pneumonitis, airway obstruction by foreign body, exogenous
  lipoid pneumonia, interstitial fibrosis, and aspiration pneumonia with
  or without lung abscess formation. Many patients who aspirate do not
  present with disease, suggesting that pathophysiology is related to a
  variety of factors, including decreased levels of consciousness,
  dysphagia, impaired mucociliary clearance, composition of aspirate,
  and impaired host defenses.



2014 - Aspiration-Related Lung Diseases
2012 - Aspiration and Infection in the Elderly
2015 - Pediatric foreign body aspiration: A nidus for Aspergillus colonization
2012 - All that wheezes is not asthma: a 6-year-old with foreign body aspiration and no suggestive history