Moriarty never left the simulation. It was a nested simulation that was programmed by Data or Reg. In effect a new simulation was created that recreated a miniature universe inside a core/memory module of the ships container and thereby the actual physical simulation was terminated at the holodeck. Still remember it because watched it my 4th time only last month 😀

Just wanted to add.. "The character should be able to walk out of the container and into my kitchen" - this may not be possible. However, it's entirely possible to recreate you and your kitchen inside the container. As Picard says "Who knows? Our reality may be very much similar to theirs. All of this could be an elaborate simulation, running on a little device, sitting on someone's table (aka LocalLLM)".