No, usually it's the other way around...the constitution grants all legitimate powers to the federal government, not rights to individuals. Strict constructionists keep critical pressure upon the federal government to keep it from expanding and keep peoples' rights intact-- loose interpreters find justifications and loopholes that allow for irreversible government expansion and even make the specifically listed rigths to be protected carry less weight.
Those who favor loose interpretation often do so to lessen the protection of an individual's rights, while at the same time they broadly interpret the limited powers granted to the federal government at the expense of the individual and the states. The whole point of the constitution was to specifically grant powers to the federal government and otherwise limit it--if it is interpreted broadly then the constitution is made practically impotent, as is any contract that is not considered within the bounds of the original intent to which it was created and agreed upon. The people's check on the growth of central power is threatened by loose interpretation of the constitution.