It can happen in some instances but this isn't one of them...
The most common time for PPs is during initial public offerings (before or after). If a company does not raise the amount of capital it wished for during the IPO and the IPO stated that the desire was to issue 1,000,000 shares and only 500,000 shares were issued, the remaining 500,000 shares are available for private placement. Private placements are most often required to be distributed to "sophisticated" investors. "Sophisticated" is used as a legal term in this instance, also.