The visible thread-like mass of DNA and its associated proteins in a eukaryotic cell that is not undergoing mitosis is called chromatin.

Here's why:

* Chromatin is the complex of DNA and proteins that makes up chromosomes in eukaryotic cells.

* When a cell is not dividing, the chromatin is loosely packed and dispersed throughout the nucleus. This allows for access to the DNA for processes like transcription (copying DNA into RNA).

* During mitosis, the chromatin condenses and becomes more tightly packed, forming visible chromosomes. This organization helps ensure that each daughter cell receives a complete set of chromosomes.

So, while chromosomes are the most visible during mitosis, the underlying structure of DNA and its associated proteins is always present as chromatin, even when the cell is not dividing.