to dig out ?

There are Hasidic tales told of similar mix-ups, in which it was taught that the "secular" person was more deserving of burial in that designated spot than the "tzadik" it was reserved for. Some soul-searching is called for and the righteous deeds of both deceased should be examined.

there was a woman whos children were anti religious and because they married nonjews she always bothered them. They fought with her until her last day and promised her that when she would die they would cremate the body. She passed away and the nursing home accidentally misID'd her and identified the wrong family who gave her a religious burial. A week later the religious woman who was mistaken to be dead and buried called her children upset at them for not coming to visit her. They were shocked to hear from her after they buried her. Once the mistake was cleared up the children of the real women who died heard from the friends of their deceased mother of how she prayed every day to have a kosher burial and not to be cremated like her children threatened.

as the custom, lest he will be snatched by the non-religious to Abu Kabir for autopsies.

two bodies mixed up due to human ineptitude.

now the secular man is the one who buried and also the one who has been exhumed, the religious man was not absolutely offended. The relatives of the secular man were paid for that mistake by having a FREE kosher burial. So, don't deduce money from the double funeral fee of the Rabbi; everything kosher is costly.