In many cases, the sibling who leaves home will encounter a gradual adjustment period. They may feel a sense of loss at first, but eventually they'll learn to cope and adjust.
It's common for siblings to communicate more effectively when they're not living under the same roof. This can help them to resolve any conflicts that might have arisen while they were living together.
If there are financial hardships involved in the sibling leaving home, their parents or other family members may be able to provide assistance.