This is usually seen in clinical settings: a child is left with an untreated enamel caries. Then the lesion progress and the lesion is cavitated. The dentin then start to react, ocludding the dentinal tubules. When the saliva (+ minerals) reach the dentin, the caries process start to slow down and the dentin change from dark brown to almost black. At the same time, the change in color represents a change in the surface composition, changing from a soft surface to a hard one.
This occurs with the minerals of the saliva. If you add fluoride, you will enhance this process. Hence, the fluoride of the toothpaste will slow down the caries process in the dentin.
About you side question: often. Keep in mind that any radicular surface clinically visible means exposed dentin. Google "radicular caries" images.
If you want to read the details, ten Cate has several (now classics) papers:
- ten Cate JM. Remineralization of caries lesions extending into
dentin. J Dent Res. 2001 May;80(5):1407-11.
- Deng DM, van Loveren C, ten Cate JM. Caries-preventive agents induce
remineralization of dentin in a biofilm model. Caries Res. 2005
Bonus 1: nobody knows why the carious dentin is brown...
Bonus 2: a black spot in a teeth means a dentinal stopped carious lesion.