If a person is in galus (ir hamiklat), what is his chiyuv regarding bringing a korban he is chayav for?
Avraham Yitzchak Marcus
The inadvertent murderer in the Ir Miklat is not obliged to leave in order to bring a Korban he is Chayav for.
See Mishnah Makos 11b that he must never leave the Ir Miklat. See TIFERES YISRAEL # 49 that he does not leave the city to go up to Yerushalayim on the 3 Yomim Tovim. OR SAMEACH HILCHOS ROTZE'ACH 7:8 explains that the reason for this is since the Go'el ha'Dam is allowed to kill him if he leaves the city, a person is not obliged to put himself into danger even in order to save the whole nation (even if he was the commander-in-chief of the army). Therefore he certainly should not put himself in danger in order to bring a Korban.
However, it would appear that he should send his Korban to the Beis ha'Mikdash with a Shali'ach. See TOSFOS MEGILAH 3a DH EMESH who implies that even if the owners are not present, the Kohanim can still bring the Korban. This is also stated by RASHBA there. However, TUREI EVEN there, DH EMESH, asks on this from TA'ANIS 27a, "How can a person's Korban be brought if he is not standing by it?" However MEIRI TA'ANIS writes that the Korban is Kosher even if the owners are not present but ideally we wait for the owners to arrive. Therefore, in the case of the murderer in the Ir Miklat, since it is not possible to wait for him, the Korban he sent may be sacrificed in his absence.