I was reading up on the stable marriage problem and chanced upon this question: Is it possible that a man1 has woman1 on the top of his preference list, and woman1 has man1 on top of hers, but still there exists a stable matching (not necessarily man optimal or woman optimal) where they are not paired together?
Stable Matching Algorithm
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The case you are describing sounds like one that is stable but not strongly stable.
From "The structure of stable marriage with indifference": A matching M is strongly stable if there is no couple (x,y) such that x strictly prefers y to his/her partner in M, and y either strictly prefers x to his/her partner ... For a given instance I of SMP, the existence of a weakly stable matching is guaranteed: ... On the other hand, it is straightforward to construct instances of SMT which admit no strongly stable matching.
So it sounds like the answer is yes... it is possible.