Finding the motive is subject to further investigation.

the subject of an investigation.

They were obviously illegal. It should be a subject of this investigation.

After further investigation, the juvenile admitted that he had made the whole story up.

Just being referenced in an F.B.I. file is not tantamount to being the subject of an investigation.

The problem was that it was very difficult to deal with the special prosecutor's investigation of the CIA leak. While it was going on we decided not to put me on the air. After the Libby indictment they extended the prosecutor's term, so I never went back on the air.