Foods often DON'T stay fresh longer when kept in the original packaging after opening, compared to careful re-wrapping in appropriate materials. The original packaging may retain moisture, juices and/or preservatives, may prevent air circulation, and may maintain relative sterility until opened. However, once opened, it may be better to re-package the remainder after some of the food is removed.
Food freshness is best retained by closely wrapping or packaging food to preserve the desirable qualities, and to prevent contamination.
Some examples:
Sliced cold cuts can lose moisture and be inoculated by undesirable bacteria unless closely wrapped in impermeable kitchen wrap. Attractive curled placement facilitates spoilage, and slices should be layered, flat, offering minimal exposed surfaces.
Canned foods can lose flavor, be contaminated by bacteria or by chemical reaction of air with the metal can, and thus do better in a glass or plastic container with little airspace or with added brine or juices.
Breads, buns and pastries will last much longer, fresh and without mold, if an airtight plastic bag is used to enclose the original packaging, with most air removed.
Frozen foods suffer "freezer burn" if kept in original packaging that allows cold, dry air to cause dehydration and ice formation from the food.