In (Metropolis) Monte Carlo one should be generating random changes in coordinates such that
\begin{equation}
X_{new} = X_{old} + \Delta X
\end{equation}
and we used a random number to generate $\Delta X$. So by all means, the particles have no reason to stop at a boundary provided the $\Delta X$ tells them to cross it. I don't know how one would keep particles inside a boundary without periodic boundary conditions.
If one was to bias the generation of $\Delta X$ in some way, we would probably not be maintaining detailed balance
There are cases where particles cannot cross a boundary, however, one needs to account for a physical boundary, such as in a nanopore or molecular sieve, by making a real boundary that interacts with particles.
If there is no periodic boundary conditions, rather than simulating a bulk fluid we will be simulating some cluster of molecules with a very real surface tension contribution that cannot be ignored. Some people study droplets, so this makes sense. However, if we want to study bulk fluids, we cannot have a system with such a large surface tension contribution.
It is a good idea to compare the simulation with what one is trying to model, and make sure the simulation reflects the reality of ones interests.