I used to have this exact same issue in Sheetcam. It would come back at the very end of a file, after my perimeter/interior detail was cut, and start cutting another interior detail. It did not show as a numbered pierce point in the toolpath, or anything. Just had to notice a pierce with no #, or lead in/ lead out if I was using those. @#[email protected]
In order to avoid this issue (among others), I've adopted the following process: Once I'm happy with general layout, and I need to start "fine tuning", I'll set my line width at (a minimum of) 1.5x my kerf size. By doing this, at any point where the lines are just kissing, I SHOULD have 1.5x my kerf width between the centerlines of the path. On my machine, that should be enough to prevent a blowout. So, if any spot in my drawing has 2 lines touching, I know it might be an issue. I adjust the spacing until the lines are not touching. Then, I should be able to avoid burn-through, as well as making sure the kerf can make it through any gaps (such as your a, above).
Take this lower case v:
Looks good, right? Let's change our line width to .07:
Whoops! We're going to have a problem here. See how the lines overlap? This is potential burn through/inability of the kerf to get through the opening. In this case, it could cause exactly the issue you're having with your "a".
Let's use the node tool to spread the lines, until there is a slight gap between them:
Since we have a slight gap there, we should be good. It may be close, but we shouldn't have burn through. You'll have to test with your machine to see exactly how close you can get. If you want to make SURE there's not a problem, open the lines up even further (or set your line width thicker...say, .09 vs .07).
Now we can go back to thin/hairline/no-width, which I use for drawing. We should be good to go! I do this to my ENTIRE drawing before cutting. It's a quick, effective way to look for kerf-width/cutting/path issues, without having to scrap any material.