Yes, tires can go bad when laying to long. This is more an issue with asphalt tires than with carpet tires, because on carpet you always have plenty of traction.
A tire is gone too far when it's showing cracks. If it's just slightly dried up and not so grippy anymore, usually cutting them brings up a fresh patch of rubber again.
Trinity's tire tweak also helps a little. Sauce the tires in with it and just let em dry. Not perfect, but might restore an old set of tires to active training duty again.