Question: who signs a CRL if the CAcertificate, that signs it, is immediately revoked?

["Simonato Carolina" <carolina.simonato@xxxxxxxxxxxxx>]

Hello all!

Suppose a simple situation in which a certificate chain is constituted
only by two certificates: a trusted (by some important authority) root
certificate (self-signed) and an end-entity certificate, signed by that
root certificate.
The same root certificate also signs the certificate revocation list (a
unique crl that contains all revoked certificates- for all reasons).
The problem is: who signs the crl when the root certificate is
immediately revoked, because of, for example, cacompromise?
Probably it is necessary to create a new couple of keys (and so a new
root certificate) and sign the crl with the new  ca private key?
Or is it possible to create a couple of  CA keys to sign only
certificate revocation list and not to make provision for revoking this
last  ca root certificate?

I would like to riceive suggestions about this topic.
Thank you in advance.

regards
Carolina