What is incumbent upon one who entered into a state of ihram for umrah and circumambulated, then interrupted the circumambulation and returned to his home, neither exiting the state of ihram nor slaughtering, and thereafter passed away?

Interrupting the circumambulation (Tawaf) before its completion and exiting the state of Ihram is impermissible. Whoever enters into a ritual (Nusuk) is obligated to complete it. The deceased should have returned to complete the 'Umrah. If he was unable, he falls under the ruling of one who is prevented (muhsar) and is obligated to offer a sacrifice (hady). If he is unable to do so, he must fast ten days. He must also avoid the prohibitions of Ihram.

Scholars differ regarding the completion of the ritual for one who dies while in the state of Ihram. The soundest opinion is that the ritual is not completed on his behalf. However, if the 'Umrah was an obligatory duty of Islam and he did not perform it despite being able, it must be performed on his behalf from his estate. It is permissible for another person to perform 'Umrah on his behalf from their own private funds.

What the deceased did regarding the prohibitions of Ihram, if he was ignorant, then there is nothing upon him. But if he was aware, then he is obligated to pay a ransom (fidyah) for each prohibition. This fidyah is to be paid from the estate and is not waived by death.