I've jarred soup with my pressure cooker. I know what a failed seal means, its gone bad. I have several jars which appear from the outside to have air displaced within a thickened body of soup and some off odor as though they have gone down the road to fermentation, however, the seals are completely sealed hard. Is it possible that they are not safe for consumption even though the seal is entirely intact?
It's completely possible. Sealing by itself doesn't preserve the food, effective processing does, then the seal keeps it from regaining any microbes which could cause spoilage.
If your food is sealed and gone bad then your processing is at fault - it didn't reach the necessary temperature for a long enough time.
You are using a process known as "canning". (That you are using jars rather than cans is mostly immaterial; the purpose and principles of the process are the same.)
Canning preserves food by keeping microbes out; that's the purpose of hermetically sealing the cans (jars). However, in order for this to be effective, you must also eliminate any microbes already present. This is the purpose of cooking the food in the cans (jars). Such food is then effectively "sterile".
Cans (jars) go bad when microbes get into the food and start doing what microbes do, which includes producing gas. This is why you see "discard if button is raised" on canned goods; the 'button' is an indicator that the pressure inside has increased due to microbiotic activity producing gas.
Any sign that microbial activity is happening or has happened inside the can, or that microbes may have been introduced — bulging, odors, leaking, failed seals, fermentation — means the contents are no longer sterile, and consuming them is probably no different than if the food had sat, open, on your counter for however long since the food was canned. It might not kill you, but you'd be taking a pretty big risk. Thus, any canned (or jarred) food showing any such indications should be assumed "bad" and discarded accordingly.
As another answer noted, if the seals are good, you probably didn't process the jars properly, resulting in microbes still being present from when you filled the jars. It is absolutely possible for this to happen and for the food to be unsafe.
For comparison, consider homemade beer. Although those bottles need to be sealed in much the same manner, they are most definitely not sterile. In this case, great care is taken to ensure that only desirable microbes are present (resulting in fermentation and carbonation) inside, but it's a good illustration of how "properly sealed" doesn't equate to "sterile".