What you have is a Mammillaria carmenae (spelling?) planted in peat, that died. Peat expands when wet, then shrinks when it dries. This constant stretching does wonders for tiny roots. Eventually, one breaks, and eventually a fungus finds one of the broken roots. To prevent this, the ideal situation is to soak the plant in a bucket of water when they are first bought until the whole root ball is wet through. Swish them around (gently) until most of the peat falls off, then re-pot into better stuff. I have had them die several years later because the nugget of peat against the stem finally rotted the plant. Grrrrr. Learning can be painful.

Oh no :( thank you for your help. Do you have any advice on repotting my 3 surviving cacti. I'm so sad to loose this one just before I was about to repot. The soil ive got for repotting is a cactus and succulents mix (upon investigation it does have 50% peat in it) and I was going to add horticultural sand to that mix . Willthat mix be ok or should I seek out an alternative mix. Should I soak the cacti when repotting to get rid of all the old soil I'm a bit weary of exposing them to too much water . i had no idea until recently that the soil the shop puts them in is so bad.