C172 Instructor reported taking evasive action while on approach to a non-towered airport to avoid non-communicating aircraft.

Narrative

Instructional flight; VFR practice instrument approaches in VMC; ZZZ LOC XX. Aircraft X joined the localizer course inbound about 2nm south of ZZZZZ then descended down from FAF at a standard rate. 2 position calls were made by Aircraft X during the descent to the field while on the approach. No other calls were heard from other aircraft. Instructor on Aircraft X was monitoring traffic visually; with G1000 TCAS; and Sentry reporting. Visibility conditions were VFR; but noticeably hazy due to smoke traveling North from a local fire. While descending through 1100' MSL; the CFI in Aircraft X first noticed an oncoming aircraft visually; at the same altitude less than 300' head on. CFI immediately exchanged controls; and used evasive maneuvering to the right to avoid midair collision. After establishing a turn; the oncoming Aircraft Y seemed to see Aircraft X and made their own offset turn to the right. Neither student or instructor in Aircraft X heard calls from the aircraft; or ever saw them digitally by TCAS or Sentry. It is not known if this aircraft was departing ZZZ or transition south at a low altitude (visually they were offset of a straight out departure* which also made them harder to spot). Review after the flight using information confirmed this aircraft was never reporting their position.