"Use by" is typically for an unopened container, as they have no way to control for how you have stored it or possibly contaminated it with other ingredients after opening.
The specific risk of garlic is that Clostridium botulinum spores are pretty commonly found on garlic. These spores are hard to kill, although commercially-prepared canned garlic has usually been processed hot enough and long enough to do so or you hear about recalls. However, that is typically after someone gets ill.
The general risk of any food left in refrigeration long-term is that when you remove it from refrigeration, scoop out some, and return it 1) how long was it outside of refrigeration and what temperature did it get to, and 2) did you contaminate it with anything that might now be growing, albeit gradually, in the refrigerator.
If it is bubbling, definitely throw it out. If it smells bad or unusual, definitely throw it out. Otherwise, there is an ever-increasing risk the longer the opened jar is in the refrigerator, influenced by how it has been previously handled, but specific information is not readily available on the USDA or FDA websites for this product.