Hold a charge near a grounded metal sheet and the sheet does not stay neutral: free electrons rearrange until its surface is a single equipotential, dragging an answering film of charge to sit beneath the intruder. Solving for that induced film directly is a genuinely hard boundary-value problem.
In 1848 William Thomson (Lord Kelvin) found the trick. Delete the conductor and drop a single image charge −q the same distance on the far side. In the region above the plane the two-charge field is identical to the real one — same field lines, same surface density σ(ρ) = −q d ⁄ 2π(ρ²+d²)^{3/2}, and the same total induced charge, exactly −q.
Why is one guess allowed to stand in for a whole rearranging sheet? The uniqueness theorem: a field that satisfies Laplace's equation and matches the boundary values is the only one there is. Find any solution and you have found the solution — mirror and all.
The simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.