Recovering files after switch_root

So, I have an embedded system running a Linux distro. It has a key (RSA) in an intermediate stage and then calls switch_root. switch_root recursively deletes the files on the host filesystem, but I don’t think this is a secure delete, so it seems to me that the new filesystem should be able to recover files from the precursor including that RSA key. I am verifying the security of this system, and don’t think it is secure because of this flaw, but I am unable to prove it.

Halp? Pls?