The horn will continue to grow and if it's heading towards the head the tip can grow into the flesh and bone. It's gruesome but very easy to prevent. You can't cure it, but you need to take the tip off the horn, and keep doing that every time it grows. The horn will be quite weak and wobbly when she's young, but will gradually grow more firmly. Initially you can remove the tip with big loppers or similar, or serrated hoof shears but when the horn has thickened a cheese-wire type saw is better. Check how much of the horn has a blood supply - the tip is always cool, the part with a central, live core is always warm. At some point the warm bit will change to cold and that is the bit you can safely cut back to. Don't try to take the whole thing off down to the head in one go. Sometimes these weak horns or scurs are so weak that they get knocked off in the lamb scrum, or when you round them up. If it's bleeding you can apply something to stop the bleeding - we use cobwebs, but there are various products sold for humans which can also be used, but good idea with horned sheep to have something available. Sometimes an artery is torn - just apply heavy pressure for 5 minutes or until it stops, or if you can see a torn mini artery bleeding you can pinch the end again for 5 minutes. Stop the bleeding, spray with antibiotics and apply Crovect or similar at the normal rate.
Sorry this all sounds traumatic - it's not really, I'm trying to cover all the possibilities.
In our experience a weak horn or scur is not inevitably passed from dam or sire to the offspring, and you can in fact get some sheep with superb horn sets from such ewes. We feel scurs and non-Jacob type horns are part of the Hebridean breed. They are not Jacobs which need the two horns which don't tip forward at all - hence the horrible specimens you occasionally see at shows with horns tipped right back and crossed behind the head, or very radically pruned horns.
If two neighbouring horns fuse there is no problem. She won't have a well balanced hornset but not every 4 horned Heb female does. If it happens in a male you wouldn't use him for breeding, although there is no research-based knowledge on the subject - A tup with well fused horns would definitely not do well in the ring, but there is no problem with his health.