At pages of Gemara 57ab, see Mishna and Gemara:
Mishnah: A karpaf is allowed for every town; so R' Meir, but the sages ruled: [the law of] karpaf was instituted only between two towns so that by adding to each one a stretch of land of seventy and a fraction the karpaf combines the two towns into one. So also where three villages are arranged in the shape of a triangle, if between the two outer ones there was a distance of a hundred and forty-one and a third cubits, the middle one causes all the three of them to be regarded as one.
Rabbi Meir says that each town has around it a strip of 70 cubits and a little.
Rabanan say that this strip, called "Karpef" is only between two quasi-adjacent towns, and his scope is to unify them. For Rabbanan, two opinions in Amorayim:
- Following Rav Huna, one Karpef for each town. So, when the distance between the two is 141 cubits approximatively, we can unify the both. (Tosfot say in name of RI that davka 2 towns are needed for 141 cubits).
- Following Chyia Bar Rav, one Karpef for the both, So, when the distance is 70 and a little, the towns are unified, not furthest.
- Rabbi Meir allows between two towns, with a distance of 141, even following Chyia Bar Rav. For one semi-circular town I don't know.
- For Rabbi Meir, we can answer for a semicircular (horse shoe shaped) town if he gives between the extremities 141 or 70,
- For Rabbanan if they give, following Rav Huna (ruled as Halacha, see Tosfot in name of Rabenu Tam) 140, or nothing; for Chyia Bar Rav 70 or nothing.
I do not remember the OP case in Gemara, and I am not sure, but see here the Tosfot in name of Rashbam. Superficially it seems that Lav Davka 2 towns, but all cases in which the purpose is to go from one to another. So in one town you can go from one to another through inner streets. But it is very length, may be that it is allowed. But may be also that if there is already one allowance to travel from the first extremity to the narrowed second extremity, no karpef is needed. (The last possibility is my provisional answer).
There is a Gemara daf 61a about a semi circular town, but the purpose is about 2000 cubits, allowance for 4000 cubits from 1 extremity to another; not about karpef. There are additional sugiot regarding a shorcut from one point of an underground habitation to another . But here, for karpef I don't found more.