Pastilushka is a dried fruit product, so its texture depends a lot on humidity and temperature. If the pack is left open in a damp kitchen, the slices may become sticky on the surface; in very dry air they can turn harder and more brittle. To keep them close to their original chewy texture, store the pastille in its original packaging if it can be resealed, or transfer the pieces to an airtight container.
Find a cool, dry cupboard away from direct sunlight, sources of heat like the stove or radiator, and strong-smelling products, because dried fruit can pick up odours over time. Take out only the amount you need and close the pack again quickly. Refrigeration is not necessary, and condensation can introduce moisture, so a pantry cupboard is usually a better choice.
The 800 g pack is large, so how long you take to finish it may vary. Always respect the best-before date printed on the label, and if the product smells sour, shows mould, or has an unusual texture, discard it rather than trying to salvage it.