In STEM fields, are ten-year, funded PhDs an exceptional case or more common than we think?
In the United States, long PhDs (taking more than 10 years) are a minority of STEM PhDs, but not exactly "exceptional" either. See image below, which shows percentage of 2006-10 doctorate recipients taking six years or less and more than ten years to complete their degree (via data collected in the Survey of Earned Doctorates):



(Image via MLA Office of Research blog)

In many US departments, if a student is making progress towards the degree (not just wasting resources), is a contributing member of the department, and funding is available, there is no general reason why the advisor can't continue funding if the degree takes longer than expected. Without funding, the student is much less likely to complete the PhD, which is an undesirable outcome for both the student, the advisor, and the department. 

(In some parts of the world, there may be regulations that make it impossible to keep funding a PhD student for that long. Even in the US, some departments may set a time limit on PhDs, and/or on eligibility for some sources of funding.)