A subject can become a target, and this happens all the time. The subject/target distinction is not a statement about whether a person has done anything wrong; it's only a statement about how much information the prosecutor has linking you to a crime he is investigating. That means that the subject himself need not do anything to move from one category to the other.
Here's guidance from the DOJ's manual for U.S. Attorneys:
It is the policy of the Department of Justice to advise a grand jury witness of his or her rights if such witness is a "target" or "subject" of a grand jury investigation. See the Criminal Resource Manual at 160 for a sample target letter.
A "target" is a person as to whom the prosecutor or the grand jury has substantial evidence linking him or her to the commission of a crime and who, in the judgment of the prosecutor, is a putative defendant. An officer or employee of an organization which is a target is not automatically considered a target even if such officer's or employee's conduct contributed to the commission of the crime by the target organization. The same lack of automatic target status holds true for organizations which employ, or employed, an officer or employee who is a target.
A "subject" of an investigation is a person whose conduct is within the scope of the grand jury's investigation.
So the designation changes when the prosecutor has enough information to change it, not necessarily because the subject has done anything new.
Imagine a prosecutor investigating a bank robbery. He watches surveillance footage showing a man checking out the bank repeatedly in the days leading up to the robbery. That's enough to bring him "within the scope of the investigation," but it's not really damning enough to link him to the crime or make him a defendant.
So he remains a subject, and the FBI continues to investigate. All sorts of things could happen that might make him a target:
- someone else implicates him;
- video footage shows him robbing the bank;
- he admits to the crime;
- he denies the crime with an alibi that doesn't check out;
- he lies about something else, making him a target for making false statements to a federal investigator.
Note that the change could come because of something the subject did himself, because of something someone else did, or just because the prosecutor happened upon some new information.