No there are none. After not matching last year, I contacted the ACGME and here were the replies I received:

Reply 1:
The ACGME expects all residents who are appointed to approved positions in accredited programs to be provided with funding that permits them to concentrate on being a student. Further, we expect all residents to be appointed in accordance with institutional policies and procedures. Finally, if some residents are paid and other provide their own funding, it sets up a two class system of resident, which is not good for education.

Steven P. Nestler, PhD
Executive Director
Residency Review Committee
515 North State St, Suite 2000
Chicago, IL 60126
312.755.5025
spn@acgme.org

Reply 2:
No, you cannot be a self-funded resident. No program would let you, because it would violate our institutional requirements.

billy

Billy Hart
Accreditation Administrator
RRC for Orthopaedic Surgery
312.755.5026