Perhaps the initial energy was bound to the strings in their creation, it originated with the strings themselves, or it would gain energy by interacting with other strings, other particles. It is considered a closed system, because even if it began as an open system, the endpoints could still meet and create a closed system, therefore there can be no string theories that do not involve a closed system. As to the how, the endpoints meet creating a loop, an infinite sequence that must be closed, or else you would follow it to infinity, like the ant walking a mobius strip.
Was this any help, or am I barking up the wrong tree?