Last summer we had a sewer smell and an epidemic of sewer flies in the basement. There was no backup of water or sewage to indicate a blockage – just an odor and a lot of pforish flies. We called a plumbing company which sent someone out to rout the main drainpipe and examine it with a camera. Although there were no cracks detected in the pipe, he said there were "rocks" in the line and recommended bringing in a jetter. The next day the drain was jetted. Immediately afterward the plumbing contractor said we needed to excavate the entire drainpipe, out to the street (tearing out walls, paneling, putting a hole in the foundation, etc.) at a minimum cost of $20K. We decided to wait to see what effect the jetting had. Meanwhile, the plumber left in a huff saying, "Don't have any big parties." We noticed that the concrete around the stack in the basement was cracked as a result of the vibration from the routing and jetting and the floor around the drain was seeping as a result. We removed the cracked concrete from around the stack. How do we fill the gap between the floor and the stack? The house is about 85 years old, as are the other homes in our historic neighborhood. I can attach a photograph 
How to we repair cracked and broken concrete around a sewer stack in the basement floor
drainsewer
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Here's my speculation, based on your description and my experience. It is just a theory. Do not commit any resources based on this without collecting corroborating physical evidence supporting it. A direction to investigate at least.
The main floor plumbing goes out to a septic tank. The pipes were not placed lower because there was no need, it just meant digging deeper outside. No one wants to do that without good reason.
When the city sewer was installed, the basement construction tied into it, but the old plumbing was never redirected, it remained on the septic tank. Not the best scheme and possibly illegal, but I'm not surprised someone did this.
It is highly probable there is nothing below to the basement to tie into. The sewer may not be much lower than the basement drainage exit. Anything placed lower than this will likely need to drain into an ejector pumping chamber.
If the pipe itself is in good enough shape, you could just use a compression cleanout plug (sometimes called a mechanical cleanout plug) or a pressure testing plug:
There are quite a few different styles of these, but almost all of them work by compressing and expanding a rubber gasket inside the pipe. 2.5" might be hard to find at the big box stores, but they are available numerous places online. The main consideration would be finding one that would seat deep enough into the pipe that it would be beyond the notches for the old cap.
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Best Answer
The right way to do it is dig out and repour the concrete in the area. This isn't that hard or expensive.
If you want just a stopgap until you decide what you are doing with your main line then you could get a bucket of hydraulic cement and patch over the existing concrete. The cracked concrete should not be affecting your stack - hopefully - so this is really a different issue than your plumbing problem.