Numerical simulation for a bounded process. Is slight deviation a "normal" fact?

Suppose I have to numerically simulate a process ${y_t}$ such that $y_tgeq0$ $forall tinmathbb{N}$, with $t$ denoting time-step.

Let’s suppose I use MonteCarlo with $mathscr{N}$ simulation trajectories. Could it occur that sometimes, when running simulation, some of these $mathscr{N}$ trajectories slightly goes beyond $0$ hence violating the condition of non-negativity of the process?
I mean: should I take this fact as an alert around the incorrectness of my simulation code or is it allowed that numerical simulation can (just "sometimes") give you some trajectories (out of the total $mathscr{N}$) that slightly deviate from the non-negativity condition?