Non-shadowing conjecture for chain-recurrent sets with attached hyperbolic singularities

Let $M$ be a closed manifold and let $X$ be a $C^1$ vector field on $M$. Let $\Lambda\subset M$ be a chain-recurrent set with an attached hyperbolic singularity. Hyperbolic attached-singularity non-shadowing conjecture. Then $\Lambda$ does not have the shadowing property. This is presented as a weaker conjecture toward the broader assertion for attached singularities. Its status is not resolved by the supplied text.