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The classification of a security breach that employs brute-force methods to compromise a system is classified as attrition. This type of attack typically involves an attacker attempting numerous combinations of credentials in order to gain unauthorized access to a system. Attrition, in a cybersecurity context, refers to the gradual weakening or erosion of defenses over time, often achieved through repeated attempts to breach security, like those seen in brute-force attacks.

The other classifications do not accurately describe this scenario. Impersonation involves an attacker taking on the identity of a legitimate user to gain access or perform malicious actions; this is not applicable when describing brute-force attacks. Improper usage refers to legitimate users abusing their access rights, which does not apply to an external attacker using brute-force tactics. Loss or theft of equipment pertains to physical security incidents where devices are stolen or lost, which is unrelated to the method of compromise described in the question. Thus, attrition is the most fitting classification for a brute-force security breach.