In the previous Mishnah we learned that a husband may exempt his wife from taking an oath, and that his exemption covers even the oath she would owe to his heirs. Our Mishnah continues with this same scenario.
The case in the Mishnah:
A woman whose husband exempted her from an oath, "halchah mikever ba'alah l'veis avihah o shechazrah l'veis chamiha" - she went from her husband's grave back to her father's house, or she returned to her father-in-law's house, and she was not placed in charge of any of the property after her husband's death. In other words, nothing new arose here: all of her financial involvement took place earlier, during her husband's lifetime.
Therefore, since her husband exempted her from an oath, the heirs cannot impose an oath upon her when she comes to collect her kesubah, neither regarding her kesubah nor regarding her handling of her husband's affairs - and this includes whatever took place between his death and his burial.
Why she is exempt even regarding what happened between the death and the burial:
One might have argued that this is a new matter about which she can be made to swear, since the husband's exemption applies only to matters that occurred during his lifetime. But if we were to begin imposing oaths upon her regarding the period between death and burial, which includes the financial arrangements connected with the burial itself, there would be a concern that the husband would not be buried at the proper time. She is therefore exempt: although the husband's exemption generally does not cover matters that occurred after his death, here it covers everything that takes place up until the burial.
She became an administrator after the burial:
If after the burial she became an administrator over her husband's property, the law divides into two:
Regarding the future - even though she was exempted from an oath by her husband, the heirs can impose an oath upon her regarding the matters and transactions that took place after the burial, since these were not included in the exemption.
Regarding the past - they cannot impose an oath upon her regarding what occurred earlier, during their father's lifetime, and not even by means of "gilgul" - saying: since you are swearing to us now about the new matter, let the oath be extended to include all the other details as well. Even in this manner she is not made to swear, since her husband exempted her from everything that took place during his lifetime.
In summary: A woman whose husband exempted her from an oath and who did not become an administrator - the heirs do not impose an oath upon her, not even regarding what occurred between the death and the burial, so that the burial should not be delayed. If she became an administrator after the burial - she is made to swear only about what took place from that point onward, and she is not made to swear about the past, not even by way of extending the oath through gilgul.