One thing to be aware of here is that JQL would only find issues if the sprint field consisted of at least one closed Sprint and an active sprint. Depending on how you define"Spilled over" this could be flawed; consider if an issue has more than one closed sprint and no open sprint.
in any event I found this JQL to work for me...
Sprint in openSprints() and sprint in closedSprints()
You might also consider the following JQL which would find any issues not yet complete that have associated closed Sprint...
sprint in closedSprints() and resolution is EMPTY
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