In this note, we exhibit a situation where a stationary state of Moffatt's ideal magnetic relaxation problem is different than the corresponding force-free $L^2$ energy minimizer of Wojtier's variational principle. Such examples have been envisioned in Moffatt's seminal work on the subject and involve divergence-free vector fields supported on collections of essentially linked magnetic tubes... Justification of Moffatt's examples requires a strong convergence of a minimizing sequence. What is proven in the current note is that there is a gap between the global minimum ({\em Wojtier's minimizer}) and the minimum over the weak $L^2$ closure of the class of vector fields obtained from a topologically non-trivial field by energy-decreasing diffeomorphisms. Consequently, our result applies beyond the Moffatt's relaxation to any other relaxation process which evolves a divergence-free field by means of energy-decreasing diffeomorphisms, such processes were proposed by Vallis et.al and more recently by Nishiyama. (read more)