If there is any leftover shed constricting a tail tip, and it's not taken off immediately, it will dry and strangulate the tail(meaning, no blood flow). If this is not remedied soon, the tail tip will die and fall off, possibly causing infection.

I would start soaking the tail in betadine solution and keeping it moist with polysporin(neosporin w/o pain killer). Then, get the snake to the vet so he/she can prescribe some burn cream(usually sulfadene cream) that will aid in healing and prevent infection. At best, the tail will heal with some scarring, and worst, the tail tip may need amputated.

If a snake has a bad shed, ALWAYS get the shed off of the eyes, any that is encircling the body, or any that is constricting the tail. Anything else can wait until next shed.