Some relaxed magnetohydrodynamic states of a plasma, such as the Taylor or the Alfvén state are often presented as the logical end of the plasma evolution by an argument of energy minimization under some constraint. However, these arguments are unsatisfactory and the very existence of nontrivial steady states as limits of magnetohydrodynamic evolution is far from obvious. For steady solutions to exist, the forcing term must be time-independent, it is shown that in this case, either the plasma undergoes constant change at a positive minimum rate or it comes arbitrarily close, in the quadratic mean norm, to the set of steady solutions of the magnetohydrodynamic equations.