Side seal lids would come off the jar without a vacuum. Threaded or twist-on lids would remain on the jar, but would lose their hermetic seal. Most threaded or twist-on lids have a panel in the center which loses its concavity with loss of vacuum. Plastic pouches would tend to balloon. Plastic tray covers would swell.
Cans exhibit various degrees of swelling.
These are known as hard swells, soft swells, springers and flippers. When pressure is applied to this end, it flips in again and the can appears flat. Flippers result from a lack of vacuum. When sufficient pressure is applied to this end, it will flip in, but the other end will flip out. Gas production, and resultant swelling, may be caused by chemical reaction or by bacteria which may or may not produce toxins.