This will depend on the key schedule of the design, but they are usually relatively simple expansion algorithms. In particular the initial round keys are often the actual bits of the cryptovariable and so recovering the initial round key recovers the first bits of cryptovariable (additional bits of cryptovariable can then be guessed exhaustively with less work than guessing the full cryptovariable). It is also common for key schedules to be invertible (so that the previous round key can be computed from the current round key - this allows decryption to be implemented efficiently in small memory). This means that if we recover all of the last round key, we can usually invert the key schedule to get the penultimate round key, the ante-penultimate round key and so on, back to the initial round key (which is often the crypto variable itself). Even if the cryptovariable size is larger than the round key recovered, the additional bits can typically be exhaustively recovered with less work than full exhaustion.
All of the above does depend on the choice of key schedule by the designer, but it does apply to major designs such as AES, DES, Serpent, and Twofish.
