In Parshat Tazria (Vayikra 13:46) we are told:
All the days the lesion is upon him, he shall remain unclean. He is unclean; he shall dwell isolated; his dwelling shall be outside the camp
As Rashi explains:
He shall dwell isolated: [meaning] that other unclean people [not stricken with tzara’ath] shall not abide with him.
The source for the Judaica Press translation's parenthetical explanation of Rashi "people [not stricken with tzara’ath]" (implying that the leper may sit with other lepers) appears to be a Braitah brought in Pesachim 67A and Rashi's commentary there.
The Talmud (according to Rashi) there explains that when the verse says "he shall dwell isolated" it means that other forms of impurity (Zav or one impure by a dead body) do not have to go outside all three camps, while the "leper" must.
This seems to indicate that "lepers" may sit together, outside the camp. We see this in the story in Melachim II 7:3 as well, where there were 4 lepers sitting together at the gates of the city.
However Rashi on Vayikra 13:46 continues.
Our Sages said: “Why is he different from other unclean people, that he must remain isolated? Since, with his slander, he caused a separation [i.e., a rift] between man and wife or between man and his fellow, he too, shall be separated [from society].”- [Arachin 16b] [This rationale is based on the premise that a person is stricken with tzara’ath as a result of his talking לְשׁוֹן הָרַע, i.e., speaking derogatorily of others, although he may be telling the truth.]
If the "leper" must be isolated and separated from society due to the rifts he has caused, shouldn't he also be separated from other "lepers"? Why is he still allowed to sit with other "lepers"? Especially since the rifts Rashi (and the Talmud) mention are personal rifts, not societal rifts. Why don't we say that just like he caused people to be separated, he too should be separated and alone?