Can a recruiter contact a postdoc's recent supervisor who was not listed as a reference on the application?
At least in US academic culture, the fact that P is applying for a given position, or is applying for jobs at all, should be considered confidential.  As such, if you're the recruiter, you should not contact S or T or anyone else regarding P's candidacy, unless you first get permission from P.  (Obviously, you have implicit permission to contact A, B, C, since they were listed on the application.)

Asking S or T for a general assessment of P's abilities, without saying that they're applying for a job, is a gray area.  I would advise against it, since people will tend to infer that your reason for asking is because P is a job candidate.

If you're the candidate, on the other hand, you should be prepared for the possibility that the employer might contact S or T anyway, even though they're not supposed to.

Expectations might be different in different cultures.