We can’t guarantee that you won’t make mistakes even if you are mature welders. So, the welder community have developed some techniques to overcome them.
Melt-throughs are common in professional welding workshops, and you should be familiar with the techniques that help you fix them.
As you already know, burn-through is a minor hole in the weld joint, and you can fill it up with a small weld on that hole. If clumsy edges are around the hole, we suggest you grind them off before inserting the filler metal.