Before us is Mishnah 3 in chapter 7 of Maseches Gittin, which deals with a husband who makes his get conditional upon his death. The Mishnah distinguishes between different formulations of the husband's words, and rules in each one whether the get takes effect or not.
"Zeh gitech im meisi":
"Zeh gitech im meisi" - one who says to his wife that this shall be her get if he dies.
"Zeh gitech im meisi meicholi zeh" - that it shall be her get if he dies from this illness.
These two formulations are the same as saying "zeh gitech le'achar misah" - this is your get after death - since their meaning is that the get should take effect after he dies. Therefore he has said nothing, and the get is not valid, for there is no get after death. Both of these expressions indicate that he wants the get to take effect after he dies, and at that point it is already too late.
"Meihayom im meisi" and "Mei'achshav im meisi":
If he said "meihayom im meisi" - that the get should take effect from today on condition that he dies - or "mei'achshav im meisi" - from now, if I die - this is a valid get. The death is merely a condition, while the get itself takes effect from today or from now.
"Meihayom ule'achar misah":
If he said "meihayom ule'achar misah" - from today and after death - this is a case of doubt, and therefore "get ve'eino get" - it is a get and it is not a get. The doubt is whether by adding "after death" he retracted his first words, in which he wanted the get to take effect retroactively from today, or whether he did not retract. Since the matter cannot be decided, it is a doubt whether she is divorced.
Therefore, if he died and she came before a yavam, she performs chalitzah but does not undergo yibum:
She does not undergo yibum, since perhaps it is a valid get, and she is his brother's divorcee, who is forbidden to him.
She cannot be released with nothing at all, since perhaps it is not a get and she is bound to yibum, and therefore she performs chalitzah.
"Meihayom im meisi meicholi zeh":
If he said "zeh gitech meihayom im meisi meicholi zeh" - this is your get from today if I die from this illness - and then he got up and walked about in the marketplace, meaning that he recovered and entered a remission, and afterwards he fell ill and died. In such a case we assess him, that is, we must evaluate and determine the cause of his death:
If he died from the first illness - meaning that the original illness never really passed but was lurking behind the scenes and returned - this is a valid get, since from the outset he stipulated that if he dies from this illness it should be a get, and indeed he died from that very illness.
If he did not die from the first illness - it is not a get, since he wanted the get to take effect only if he died from this illness and not from another illness.
In summary: in this Mishnah we learned four formulations of a get that is made contingent upon death: "im meisi" and "im meisi meicholi zeh" - these are not a get, since they are the same as saying "after death"; "meihayom im meisi" and "mei'achshav im meisi" - a valid get, since the death is merely a condition; "meihayom ule'achar misah" - a doubt, and therefore it is a get and it is not a get, and she performs chalitzah but does not undergo yibum; and "meihayom im meisi meicholi zeh" - everything depends on the assessment, whether he died from the first illness or not.