Embedded bqm often has a lower energy than its original energy

I am working on problems for which i know the exact ground state energy, however, once the original bqm gets embedded into a target_bqm. Often the solver returns with energies that are lower than the ground state energy of the original model (using default chain strength and SPIN variables).

Of course, empirically : I have seen that once I unembed the target sampleset, the extracted solution in the original bqm space has an energy above or at the energy level of the exact ground state energy.

But I just wanted some clarity, is the embedding formulation such that the ground state (and others) of the embedded (target) bqm may have energies lower than that of the ground state energy of the original (source) bqm (for an equivalent solution sample of course)? Or is it designed such that the target ground state energy must match the source ground state energy?

(Related to another topic : 'Embedding returns energies which are lower than the true minimum energy', My attempt is at asking the problem from a different angle)

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