Which xiangqi pieces can never give check to the enemy general, no matter what?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws and is regression-tested against the official 110-diagram repetition casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it against the engine before publishing.
Direct answer
The advisor and the elephant, categorically. Every other piece type, the chariot, horse, cannon, soldier, and the general itself under the flying-general rule, can threaten the enemy general under the right conditions. The advisor and elephant cannot, because both are confined by their own movement rules to their own side of the board and can never come anywhere near the enemy palace.
Why this is worth knowing while calculating
When you are working out what could possibly check your general next move, you can rule out the opponent's advisors and elephants immediately and completely, not just "usually" or "probably." Nothing about the position, however unusual, changes that; it is a fixed property of how those two pieces move, not a situational judgement.
What they contribute instead
Their entire value in an attack is indirect: removing your own defender near the palace, or supporting another piece's threat, never delivering the check themselves. Every mating pattern in xiangqi that appears to involve an advisor or elephant is really the advisor or elephant enabling a different piece to deliver the actual check.
Related questions
Does this include the flying-general exception for either piece?
No, that exception applies only to the general itself; it does not extend to the advisor or elephant.
Can an advisor or elephant ever check its own general by mistake?
No, self-check from those two pieces is impossible for the same reason, they can never occupy a square that threatens either general.