To stop becoming something is to stop accumulating in philosophical sense.
Not to accumulate, but to die every day, minutely, is timeless being.
The mystics call it a kind of death.
The Stoics trained themselves in being present in the Now by philosophizing over the meaning of death in their lives.
To philosophize became in that way, for the Stoics, a way of learning how to die.
An example of this is the Stoic Horace, the man behind the expression ”Carpe diem!” (Seize the day!).