Eruvin, Chapter 3, Mishnah 4. We have already noted that an eruv - including an eruv techumin - must be accessible to the person who places it during bein hashemashos, the time at which the eruv takes effect. Our mishnah discusses cases in which the eruv is not accessible for various reasons, and cases in which it is uncertain whether it was accessible at that time.
The cases in which the eruv is not accessible:
"Nisgalgel chutz latechum" - the food that was placed for the eruv techumin rolled outside the person's techum. An eruv techumin must be placed within a person's existing techum, and it may even be placed at the very edge of the techum - thereby establishing a new central point for him, from which he may walk an additional two thousand amos - but he must be able to reach the eruv in the first place. Once the eruv rolled outside his techum, it is not accessible during bein hashemashos, and it is not a valid eruv.
"Venafal alav gal" - a heap of stones fell on the eruv, in such a way that retrieving it would require tools and digging (a shovel and the like), which are labors forbidden on Shabbos, and therefore it is not accessible.
"O nisraf" - the eruv was burned and no longer exists at all.
"O Terumah venitmeis" - the eruv was Terumah that became tamei, and Terumah that is tamei is not fit to be eaten even by a kohen; it is not fit to be eaten by anyone, and therefore it is not accessible.
The determining time:
"Mib'od yom - eino eruv" - if one of these mishaps occurred before Shabbos began, it is not an eruv.
"Mishetechshach - harei zeh eruv" - if it occurred after dark, once Shabbos had begun, it is a valid eruv, since it is enough that it was accessible at the moment the eruv took effect, during bein hashemashos.
"Ve'im safek":
What is the law when it is uncertain whether Shabbos had already begun at the time of the mishap? Rabbi Meir and Rabbi Yehudah say: "Harei zeh chamar gamal" - the person is compared to someone who is a donkey driver and a camel driver at one and the same time. The meaning of the comparison: someone standing between a donkey and a camel drives the donkey from behind, with the donkey walking ahead of him and pulling him, while the camel he must pull from in front. He is thus pulled in two directions at once.
In practice, in a case of doubt he must take both possibilities into account: it is possible that he acquired a new resting point at the place where he set down his eruv techumin, and it is possible that the eruv is invalid and his resting place is his original home. How so? When the distance between his home and the eruv is slightly less than two thousand amos (for example, he placed the eruv one thousand nine hundred amos east of his home), he may not walk east of the eruv, lest the eruv be invalid and his central point be his home; and he also may not walk west of his home, lest the eruv be valid, in which case his two thousand amos end immediately past his home. He is therefore limited to walking between those two points alone.
The view of Rabbi Yose and Rabbi Shimon:
Rabbi Yose and Rabbi Shimon disagree and hold that "safek eruv kasher" - we are lenient in matters of eruv. Rabbi Yose said: "He'id Tuma mishum chamishah zekeinim" - he testified in the name of five elders, five Torah scholars, that a doubtful eruv is valid, for we rule leniently in a case of doubt regarding an eruv. And this is the halachah.
In summary: the eruv must be accessible during bein hashemashos. A mishap that occurred while it was still day - it rolled outside the techum, a heap of stones fell on it, it was burned, or it was Terumah that became tamei - invalidates the eruv; if it occurred after dark, the eruv is valid. And in a case of doubt they disagreed: according to Rabbi Meir and Rabbi Yehudah it is "chamar gamal," and the person is limited to walking between the two points; according to Rabbi Yose and Rabbi Shimon a doubtful eruv is valid, and that is the halachah.