MDF, like most materials, can be unforgiving when drilling all the way through. This little video shows what can happen and some steps you can take to reduce blow out.
I will admit up front that MDF is not material I like to use in the workshop. Its heavy. Its dulls the blades faster. It creates a lot of fine dust. It requires safety gear. And the scraps cannot be burned. Well, you could, but I would not advise it because it burns hot and the smoke coming out of the chimney is toxic, that’s just my opinion.
I’ve burned it in the workshop’s wood stove up to today, but no more. While I had some burning, I was out in the yard doing some work and the smoking was blowing in my direction. I literally could not stay in the area as the smoke was unbearable to breath in.