Let us consider the Stochastic Differential Equation (SDE) of a process $X_t$ following Geometric Brownian Motion (GBM) dynamics with no drift and constant diffusion factor $\sigma$:
$$ dX_t=\sigma X_tdW_t \tag{1}$$
where $W_t$ is a Brownian Motion. Given an initial condition $x_0>0$, the solution is:
$$ X_t = x_0e^{-\frac{1}{2}\sigma^2t+\sigma W_t} \tag{2}$$
It is easy to see from $(2)$ that for all $t\geq 0$, $X_t>0$. But is there an intuition as for why $(1)$ would imply $X_t>0$?