The control of the cryptography is more than ever a recurrent issue. As the current international regulation does not apply in the signatory countries, the concept of enforcing backdoors in encryption system is reborn with more strength. This paper deals with a particular class of stream cipher backdoors. This class, under a different form, has been widely used by the industry in the 80s and 90s in the context of the export control rules imposed by the US to the Western countries. We propose here a new system -- called BSEA-2, with a 128-bit secret key -- which is a seemingly minor modification of BSEA-1, a system proposed in \cite{filiol_bsea1}. BSEA-2 illustrates, in a simple and didactic~\textemdash~it has been also designed for a MSc cryptanalysis course~\textemdash~but efficient way the concept of key-dependent cryptographic security. The aim is to keep control on encryption means that a country/provider could provide to another country/client for which the secret key are also provided. With such systems, changing the key class results in downgrading the cryptographic security.