No. If a declaration of nullity is made, both people are free to marry (unless a stipulation, temporarily holding-up immediate access to a future marriage, is placed on one or both parties at the time of a declaration of nullity). A negative decision, in effect, admits that the evidence does not show that the marriage bond was not properly established and binding. The parties therefore are not free to celebrate a marriage in the church. A tribunal has the task of examining whether the parties gave full and unqualified consent to the marriage and whether they had the capacity to carry out what they vowed.
The tribunal does not act as a judge of moral action. A declaration of nullity should not be interpreted as an award granted to either party, but rather a factual determination about the bond of marriage. A declaration of nullity should not be seen as a stamp of approval for particular behavior in a marriage. Declarations of nullity cannot be purchased and the review judges will not be influenced in their decision. Indeed, in the Archdiocese of Detroit, no money is requested or will be collected by the Tribunal.