Old District

The old district is a portion of Kumon-mi that is filled with dying or worthless things. It appears to be either controlled or heavily influenced by Nozomu.

Old Kumon-mi
It's possible that the old district is he actual remains of the first iteration of Kumon-mi from when it was run by Nozomu. When the system eventually failed, Nozomu was "buried" there and the entire district was depreciated, and then the new city run by the Wire God was built nearby.

Recycling Bin
The old district may instead (or in addition) serve as a location for the Wire God or the Concerned God to dump unwanted or unnecessary things. As individuals prove to be the most too weak or antithetical to the main goal of making Sensei happy, they are disposed of by "feeding them" to the old district, where they become trapped by the overbearing influence of the area. It may also be the case that as the Wire God has grown weaker over time, it's ability to manage the world has diminished and as a result the threshold for what can be maintained in the main city has decreased. This, combined with the Wire God's ever increasing weakness, may be one of the impetuses for Nozomu's return in Trinity II.

Tojo Ramen
The ramen shop operated by Tsuneyo and her father appears to serve as an extension of the Wire God is located within the old district. As one of or potentially the only access the Wire God has to Terminal 23, that fact that it is located here may have implications as to the structure of this old. If the old district is in fact a remaining chunk of the old system, then it may signal that the Wire God itself dates back to that time period. Alternatively, the ramen shop may have been placed here intentionally to keep an eye on Nozomu and the residents of the old district as they would be the most likely to cause an issue for the world as a whole. Yet another possibility is that the ramen shop is one of many access points to Terminal 23, although given the decay in the Wire God by the time Current Sensei arrives there, it's possible that Tojo Ramen is one of, if not the, last of its kind.