If you have 4'9" or similar (short) foundation walls and/or footings then digging too close to them can undermine their bearing and cause them, and your house to fall down on top of you. The soil near any foundation or post footing is what hold your whole houses weight. If you remove it then house fall down - go boom. In most cases you will have to have your whole house jacked up, your original foundation removed, the basement hole dug, new footers and foundation poured and then put the house back down. You may decide that it is worth doing this or you may want to spend your money on an addition instead of a basement room.