The answer
Yes. In ordinary BIP32 non-hardened derivation, the parent extended public key combined with one child private key can reveal the parent private key. This is a stronger risk than xpub exposure alone.
What to do next
Treat such a combination as key compromise; migrate coins with trusted recovery procedures and rotate account-level keys.
Bitcoin BIP32 specification
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Frequently asked questions
Does hardened derivation have this same child-key weakness?
No. Hardened derivation was designed to prevent this specific parent-key recovery from a child private key plus parent xpub.