Although Kohanim are generally forbidden from touching or being under the same roof as a human corpse, this is permissible in cases of the death of an immediate family member. A Kohen is allowed to attend the funeral of immediate family members and to tend to their burial. This applies even to a Kohen’s wife; if she dies, the husband is allowed to become Tameh for her burial. The Torah allows a Kohen to become Tameh in the case of the death of "She’ero Ha’karob Elav" ("his family member, who is close to him" – Vayikra 21:2), which the Sages interpret as a reference to a Kohen’s wife.
However, this applies only if they were married at the time the wife died. If a Kohen’s wife dies after they had divorced, then he is not permitted to become Tameh. The Torah allows a Kohen to become Tameh only in the case of a death of his wife "who is close to him," and after divorce, of course, the couple cannot be described as "close."
The Poskim address the question of whether this Halacha applies if a Kohen’s wife dies while they were in the process of getting divorced, but before the Get was given. Technically speaking, they were still married at the time of the wife’s death, and thus we might assume that the husband may attend the funeral and burial, just as in any case when a Kohen’s wife dies. On the other hand, perhaps once they had already begun the divorce proceedings they can no longer be considered "close," and the husband thus cannot become Tameh.
The Halacha in such a case depends upon which stage of the divorce process the couple had reached before the Kohen’s wife passed away. If the Bet Din had already finalized the arrangement, and the assets had been divided and a date was set for the transmission of the Get, then the husband may not become Tameh after his wife’s death. Even though they were, technically, still married at the time of the wife’s death, the husband may nevertheless not become Tameh, since they had essentially concluded the divorce process and were just waiting for the date set by the Bet Din. However, if the divorce proceedings had not yet concluded, then the husband attends the wife’s funeral just as he would if they had not been in the process of divorcing.
Another instance when a Kohen would not become Tameh after his wife’s passing is a situation where the wife had become a "Shota," meaning, she became mentally disabled. A mentally disabled woman cannot be divorced, as divorce requires the wife’s awareness and conscious consent. If a Kohen’s wife had become a "Shota," and they were no longer living together as husband and wife, he does not become Tameh when she dies, even though they were technically still married. As in the case of a couple that had already set a date for a Get, this couple, too, is not, as a practical matter, married, and therefore the Kohen may not become Tameh if the wife dies.
Summary: Generally speaking, a Kohen may become Tameh when his wife passes away – he may attend the funeral and the burial. However, if a Kohen’s wife died while they were in the process of divorcing, and all the proceedings had concluded, then he does not become Tameh if she dies. This applies also if a Kohen’s wife became mentally disabled and he was thus unable to formerly divorce her. If, however, a couple had been in the process of divorce but the arrangements had not been finalized, then the Kohen becomes Tameh after the wife’s death.
