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Your first statement is not exactly correct. For example, it is not possible to patch a rar archive to accept a faux serial. I have also seen programs the the author encrypted specific features of a program which could only be decrypted with a valid serial. To solve these problems, brute force is the only viable option. Depending on the length of the serial/password, it could take centuries to brute force a valid value. Hypothetically, once you get a valid serial(be it brute forced of leaked), you could nop the decryption routine and patch the correctly decrypted code into the program.
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