Chicken base does go bad if it's been opened.
However if the chicken base has remained sealed then it does not go bad as in it does not spoil to make you sick.
The chicken base does eventually fade in quality overtime and loses it's good taste so your recipe won't turn out as good with expired chicken base.
But as long as the chicken base has remained sealed and not opened it will be okay for 5 to 10 years past the expiration date.
However it's better to use your chicken base within a year of the chicken base expiration date but even better you should use the chicken base before expiration date.
So while the old chicken base may taste not as good it's still safe to eat as long as it's remained sealed.
Once opened the chicken base will last for a few days in the refrigerator.