There is a function that will control what happens to child tickets when a parent ticket is closed. That function is the “leave_children_open” option in Options Manager. When this option is installed, the closure of a parent ticket will not result in child tickets being closed. This document discusses several key items of note to keep in mind when using this option.
On whether this option can be selectively applied for certain cases and not for others:
It is not possible to have the option "leave_children_open" apply to only specific cases. The option's functionality is applied regardless of a given ticket’s elements, such as priority.
On applying a different status other than “Closed” towards child tickets:
It is not possible to specify a status other than Closed when a parent case closes out its children. The child cases will all set to a Close/Inactive state immediately.