Probably not as bad as nic
juice stored in the bottom of someone's closet in plastic bottles (with their running shoes)

Neither PG or Nicotine are inert molecules. Long term exposure to the oxygen in air will initiate some chemical reaction.
Water vapor in the air will be absorbed due to the hygroscopic properties of PG. If left open, the water absorbed will reach an equilibrium point depending on the temperature and relative humidity of the air.
At a 70 degree F room temperature, and 50% RH the equilibrium point is about 80% w/w PG.
Water absorption goes up with a higher RH.