I think this question should in fact be on Eruvin 59, not 60 as the title says, because the question appears to be why does the Mishnah on 59a (concerning the city belonging to an individual, which deals with Eruv Chatzeros) belong in this chapter?

1) The Me'iri, in his introduction to the fifth chapter of Eruvin, writes that this Mishnah is not of the same subject matter as the rest of the chapter, but some topics of Eruvei Chatzeros were included tangentially. The Me'iri does not explain why these topics were included. (However, I think that the explanations that we will bring now, b'Siyata d'Shmaya, might also explain why these topics of Eruvei Chatzeros were included, and the Me'iri does not necessarily mean that this Mishnah has absolutely no connection to our chapter, but rather that it strayed somewhat from the main topic of the fifth chapter.)

2) The Tosfos Chadashim, printed in the Mishnayos, also asks your question: this Mishnah should have come in the next chapter, which deals with Eruvei Chatzeros. He answers that possibly this Mishnah is a continuation of the previous Mishnah (end of 58b) that says that even an Eved or Shifchah are believed to tell us the location of the Shabbos boundary. We are not worried that the Eved or Shifchah forgot after such a long time where the Techum is. In a similar way, we are also lenient concerning the "Ir Shel Yachid." Even after it became a city belonging to many people, we still say that it retains the origianl status of the private city, and one may make Eruv Chatzeros in the entire city. We are not worried that a long time afterwards, people will forget that it was originally an Ir Shel Yachid and will come to say that we can learn from this city that even an Ir Shel Rabim may have an Eruv Chatzeros in the entire city and it does not require any houses to be left without an Eruv.

In other words, the fact that our Mishnah is adjacent to the Mishnah about the Eved and Shifchah teaches that we may assume that people have long memories. Just as we rely on the Eved or Shifchah to testify where the Shabbos boundary is even a long time afterwards, so we rely on the fact that people will remember a long time later on that this city was at one time an Ir Shel Yachid.

3) The Tiferes Yisrael #39 takes the connection of our Mishnah with the Mishnah about Eved or Shifchah a little further. It teaches us that an Eved or Shifchah are also believed to say that the city was previously an Ir Shel Yachid and only afterwards became an Ir Shel Rabim.

Kol Tuv,

Dovid Bloom