With tweezers and some rooting or pushing, possibly a magnifying glass and good lighting, one usually manages to pull it off. If it is broken or it is deep it becomes more difficult.
A paste (bread, butter, soft soap, bacon fat) under a plaster on the sore spot may soften the area. Or bathing. Or suck. And then try again.
Despite all the good advice to be sure not to mess around with a needle, that is exactly what I 'm always doing. I find it terribly annoying to work with. And there is a risk of infection. Even if it costs me a quarter, and painful tinkering, he has to come out. And then of course a disinfection. Or when there is nothing at hand (heu?) at least I nibble and suck it clean.