If your friend is very lucky nothing will happen for a few people they have the room for them to come in with out any issue. However that is for just a few.
So of the things that may happen can be:
1) Sometimes wisdom teeth can be painful when they are erupting through the soft tissue and can become swollen and or infected.
2) If there is no room for them to come in straight they can push or move your other teeth.
3) Making it so that not only will you still need to remove the wisdoms teeth causing the problems but she/he may need to get braces to correct the remaining teeth.