Pears are the only fruit not allowed to ripen on the tree. If a pear fully ripens on the tree, it will be soft and squishy in the middle. A pear is picked when its internal pressure is at a particular point. After picking, pears are chilled thoroughly. Following this chilling, pears are ripened at room temperature out of plastic. Once ripened, a pear should be stored in the refrigerator in plastic.