This question assumes a literal interpretation of Genesis 2-3, which not all interpreters accept but we will accept for the sake of this question. This is a question about a hypothetical scenario so I can only give a hypothetical answer.
The command God gave Adam concerning the tree of the knowledge of good and evil was:
“You may surely eat of every tree of the garden, 17 but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.” (Gen 2:16-17)
If taken as read then this implies whoever ate of the fruit of the tree of the knowledge of good and evil would die instantly (or, at least, shortly after). But neither Adam nor Eve suffer this punishment. This may be because the initial command meant “you will become mortal” or “you will be cut off from the tree of life”, rather than “you will be executed”. Alternatively, it may be that God, in his mercy, did not execute the decreed punishment but gave Adam and Eve an opportunity for salvation. If the latter option is true then this complicates matters further for this question as it means there are no hard rules.
In Genesis 3 Adam, Eve and the serpent each receive a specific curse as punishment for their actions (vv14-19). In addition Adam and Eve, who ate the fruit, are cast out of the garden to prevent them from living forever (vv22-24). If we assume God would have made the same judgment if only Eve ate of the fruit then she would have received the same curse and would have been cast out of the garden, whilst Adam would have remained in the garden without any curse. As a consequence Eve would be alone outside the garden (assuming no pre-Adamic humans) and not had any children. Adam, too, would have been left alone, though perhaps God would have created a new wife for Adam so that he could fulfill the command to “be fruitful and multiply”.
A further question is what would be the extent of the curse in this scenario. It is often assumed that the curse and its effects are passed by descent. For example, if the curse to have pain in child birth was a change brought about by God changing human physiology then this would be passed genetically. However in this scenario Eve has no children so cannot pass on the effects of the curse.