That's why I only buy my "grade" bolts from a bolt supplier or the local parts house ( not the chain stores) and all of my drill bits, taps and extractors are all made in the USA.
Ease-outs or extractors can be removed, but not by convetional methods. Unless it is really inferior junk, a drill bit won't even scratch it. I normally use a dremel or a die grinder with a burr, sort of like a rotary file, to cut them out. In my years as a heavy equipment mechanic, working in the field, I've had to get creative numerous times to remove broken bolts with what is available on my service truck.

 

If its a hardened tap or dowel or ease out, we used a tap burner in the machine shop I worked at. Kinda like a portable EDM machine. Had a mag base and a consumable tip made out of copper water flowed through the tip and electricity arced from the tip once it got close to the broken tap. These things were accurate! Wouldn't mess up the threads at all if you used the correct tip. Just had to keep an eye on it and lower the head as it burned through the tap. Probably have much better equipment for that now. This was back in the late 80's when I used it several times.