We have been in this situation. It didn't occur to us to contact the girl's parents - I think she would have been mortified had we done so. Nor did we ask her if her parents knew where she was - she seemed to be a polite and well-mannered girl so we assumed she wouldn't just walk out and let them worry.
But at sixteen, young people do have certain rights, and one of those rights is to make their own decisions regarding sex. Although most parents would want to know who their daughter is sleeping with because they care about her, the reality is that it's none of their business. It's a private matter between her and her partner, and the same applies to you and your son.
Many parents on MN seem to have got it into their heads that their sixteen-year-old offspring are still children and that they, as parents, have the right to get involved. This isn't really true, and hasn't been since 1989, when the concept of parental responsibility replaced that of parental rights.
Unfortunately - in my opinion - the actual definition has always been rather a grey area, unlike in Scotland (where a parent can only advise their 16-yo, not direct their behaviour), but my understanding of the intent is that parents should gradually transfer the right to make decisions that affect their children to their children, as the children develop the ability to make those decisions.
This followed - again, as I understand it - from the Gillick case of 1986, where under-16s were given the right to access contraception without their parents' consent or even knowledge.
When you consider that, at sixteen, young people have the legal right to leave home, live independently, get married (without parental consent in Scotland) and have children of their own, it seems clear that their own parents need to come to terms with the fact (difficult as this may be) that they are now essentially grown up and should be treated as such. Contacting the girl's parents would be incompatible with that philosophy.