Yevamos, Chapter 4, Mishnah 3. The Mishnah opens: "Shomeres yavam shenaflu lah nechasim" - a woman whose husband died and who is waiting for yibum or chalitzah, and in the meantime property came to her as an inheritance from her father's side.
On this point "modim Beis Shammai u'Veis Hillel" - Beis Shammai and Beis Hillel agree, even though they will disagree later in the Mishnah, "shemocheres v'nosenes v'kayam" - she may sell the property she inherited or give it away as a gift, and her actions stand and are valid. Even though she is waiting for yibum and may potentially marry the yavam, this property is currently under her responsibility and in her possession.
If the shomeres yavam died:
Suppose that while she was still a shomeres yavam the woman died, before the bond with the yavam was ever finalized. In other words, she was going to marry him, but it never came to be. What is the law regarding her property and possessions? This is the subject of the dispute between Beis Shammai and Beis Hillel.
The Mishnah asks: "Mah ya'asu bi'chesubasah u'vanechasim hanichnasin v'yotz'in imah" - what is to be done with her kesubah and with the property that enters and leaves with her? Three different components are under discussion here:
The kesubah - the sum her first husband obligated himself to pay her in her kesubah from her first marriage.
Nichsei tzon barzel - the property she brought into the marriage with her that was recorded in the kesubah, for which the husband accepted responsibility. He obligated himself to pay her its value at the time the kesubah is paid, whether he dies or whether he divorces her.
Nichsei melug - these are "hanechasim hanichnasin v'yotz'in imah" - the property that enters and leaves with her: property for which the husband does not accept responsibility, but from which he may benefit during the marriage. If it is an orchard, for example, he is entitled to eat the fruit of the trees; but when the marriage ends, the woman takes the property itself with her.
The view of Beis Shammai:
Beis Shammai say: "Yachloku yorshei ha'ba'al im yorshei ha'av" - all of this property is divided between the heirs of the first husband, who in this case is the yavam, and the heirs of the father, the members of her family who inherit from her, whether her father himself or her father's heirs. Both sides compete over this property.
The reason for this: since she was a shomeres yavam, her status remains in doubt - do we view her as married or not? Was the bond about to be realized? This is unknown, since it was never given the opportunity to be realized. Therefore the yavam, who is the husband's heir, receives half, and her family receives half.
The view of Beis Hillel:
Beis Hillel disagree and hold that the law depends on the nature of each individual piece of property:
"Nechasim b'chezkasan" - the property remains in its presumed status: nichsei tzon barzel stand in the presumed possession of both sides, and therefore with regard to these they do indeed divide equally, as Beis Shammai hold.
"Kesubah b'chezkas yorshei ha'ba'al" - the kesubah is in the presumed possession of the husband's heirs, for the sum of the kesubah that is due her from her first husband is in the hands of the husband's heirs, since it was the husband who was obligated to pay it and the payment was never made. For this reason he, and in this case his heirs - the yavam, hold on to it.
Nichsei melug - "b'chezkas yorshei ha'av" - in the presumed possession of the father's heirs: these remain in the inheritance of the woman's father, since nichsei melug belong to her in their essence, and even though the husband uses them temporarily during the marriage, in the end they are hers. Therefore they return to her side, to the side of her father and her family, since they are something that belongs to her and not to the husband.
In summary: In this Mishnah we learned that during the lifetime of the shomeres yavam all agree that she may sell and give away the property that came to her, and her actions stand. If she died while still a shomeres yavam, they disagreed: according to Beis Shammai all the property is divided equally between the husband's heirs (the yavam) and the father's heirs, because her status as a married woman remains in doubt; and according to Beis Hillel a distinction is drawn between the types of property - nichsei tzon barzel are divided, the kesubah is in the presumed possession of the husband's heirs, and nichsei melug are in the presumed possession of the father's heirs.