@jackiw2012 - I believe that what would probably happen in the case of missing parents, with no other living relatives available, is that first the child would be taken in by a social services officer, and possibly kept at their personal home, or in a center for foster children. They might even be dealt with (in a good way) by the local police for a couple of nights, depending on where they live (i.e. smaller areas might not have quick access to child care services).
It's possible large population centers might have a kind of half-way house available for kids who are only temporarily separated from their parents.
Then, if the parents look likely to stay missing, the child would be in foster care for at least a year or more, just in case, or while the courts process the disappearance. This could either be a facility like an orphanage (although they don't really call them that anymore) or in a private home.
If the parents are eventually declared dead, the child can be adopted.
However, this might not hold true for all states, or countries.
If you want the exact process for wherever your story is set, you should contact the local child services and ask them what their process is. You can also have a look at their website, which might have more information.