Jarred garlic is safe as long as you refrigerate the jarred garlic after opening it.
Also if you buy jarred garlic it is considered safe because if the jarred garlic actually made you sick or killed someone then the jarred garlic could not be sold.
I buy jarred garlic all the time and have eaten minced and jarred garlic for years and never have gotten sick.
I don't like to make my own because of the potential of getting bacteria in the garlic but I trust the store bought and commercially made jarred garlic.
I have never gotten sick from jarred garlic and neither has my mom either.
Many people safely eat jarred garlic and never get sick or die as a result of it.
Just make sure to refrigerate any leftover jarred garlic once the jar of garlic has been opened.