Can soft-boiled eggs be reboiled and turned into hard-boiled eggs?
In terms of food safety, as long as the egg would have been safe to eat as it is (that is, it still is in its unbroken shell, has been cooled rapidly after cooking and then refrigerated), it is safe to recook.

In terms of quality, I am not sure that you will get a very palatable result.  You are likely to end up with overcooked and rubbery whites at the very least.