The test file at https://github.com/mozilla/pdf.js/blob/master/test/pdfs/annotation-choice-widget.pdf contains listboxes, which are not rendered correctly when printed right now. These kinds of fields are made by https://github.com/mozilla/pdf.js/blob/master/src/display/annotation_layer.js#L672-L678.

/cc @calixteman 
if (pin) {
      this.pinned = true;
    }
    if (this.hideElement.hidden) {
      this.hideElement.hidden = false;
      this.container.style.zIndex += 1;
    }
  }
  /**
   * Hide the popup.
   *
   * @private
   * @param {boolean} unpin
   * @memberof PopupElement
   */
  _hide(unpin = true) {
    if (unpin) {
      this.pinned = false;
    }
    if (!this.hideElement.hidden && !this.pinned) {
      this.hideElement.hidden = true;
      this.container.style.zIndex -= 1;
    }
  }
}
class FreeTextAnnotationElement extends AnnotationElement {