The gemara says that when a sefer torah is stolen from a city, the dayanim of that city may serve as judges to convict the thief so long as they would relinquish their portion in the sefer torah. However, the gemara concludes that by a sefer torah where they will anyway be benefiting from the reading, it is not sufficient to relinquish their ownership since they will still be considered biased (nogei'ah b'davar) because they are ultimately benefiting from the sefer being returned to the city.
Tosafos asks that the gemara holds that for items other than a sefer torah it would help to relinquish their ownership thereby removing their negi'os. Why don't we require techilaso v'sofo b'kashrus? Meaning, we should require the dayanim to be kasher not only at the time of the judgement but even at the time of the crim? Tosafos answers that the requirement of techilaso v'sofo b'kashrus only applies to a passul in the guf such as a relative, but doesn't apply to a monetary passul. Tosafos in Nida 50 makes a distinction between an eid where we have such a requirement, and a dayan where we don't have such a requirement.
The Ramban explained by the Nemukei Yosef has a very interesting approach to this question. When one testifies on a monetary issue, he is not testifying on the money, rather he is testifying for the OWNER of the money. While it is true that we require techilaso v'sofo b'kashrus, and therefore one who was a relative through marriage at the time he witnessed a crime cannot testify on that crime even if he has divorced since then and is no longer a relative. The rationale is that at the time one witnesses the crime he must be kasher for eidus. But with a monetary issue such as a communal item that is stolen he is considered kasher l'eidus for all those that he is not related to, and passul l'eidus for the share of all those he is related to including himself. Therefore, by removing himself from this money, he is no longer testifying for himself, rather he is testifying for others and for them he was kasher all along to serve as a witness.
The R"I Mi'gash answers that one who is passul as a nogeiah, is not considered an eid at all. He is not like a karov who is considered an eid passul, rather he is not in the parsha of eidus. Therefore when he removes himself and becomes a valid eid, he is considered techilaso b'kashrus since that is the first moment that he assumes a status as an eid. This seems to be an exact opposite sevara from Tosafos. Tosafos considers the negi'ah of money so mild that we don't apply the din of techilaso b'kashrus, whereas the R"I Mi'gash considers it so severe that we don't even consider him to be an eid (in truth, there is a lot of discussion as to why a nogei'ah is passul. He is only passul to testify l'zechuso, but kasher l'chovaso, so he is not like a regular passul who is passul for chov and zechus. Some say it is a din of karov eitzel atzmo, some say it is a chashash meshaker, and some say he is not an eid at all - the latter seems to be the opinion of the R"I mi'gash).