If a cell loses or ejects its nucleus, what is its fate and why?
It can remain functional (for a while), but will not be able to grow or divide.
The nucleus of a cell contains the DNA with all the information the cell needs to stay alive and to divide if required. Without nucleus the cell will not be able to produce the proteins and enzymes it needs to sustain itself and it will certainly not be able to divide.
It doesn't necessarily mean that the cell is not functional. Interestingly, for some cells in the body the ejection of the nucleus (enucleation or denucleation) is a normal process . This goes for:
For other cells, it would not be favorable. That is why scientists are looking into how this (d)enucleation process can be used to treat cancer. Cancer cells can divide uncontrollably, but they would lose this ability without a nucleus.