the hearing cannot result in a due process violation. Instead, our holding requires weighing a claimant’s deprivation of an important private interest, such as unemployment benefits, relative to procedures used in such a deprivation. See Welch v. Thompson, 20 F.3d 636, 639 (5th Cir. 1994) (requiring that if there is a deprivation, “we must determine whether the procedures relative to that deprivation were constitutionally sufficient.” (citation and footnote omitted)). {27} In New Mexico, the distinguishing factor used to determine whether there was or was not a violation of due process rights depends on whether the defective notice deprived the claimant of the ability to participate in the proceeding. See Franco v. Carlsbad Mun. Schs., 2001-NMCA-042, ¶¶ 6, 14, 130 N.M. 543, 28 P.3d 531 (<HOLDING>), recognized in Lobato v. N.M. Env’t Dep’t,
holding that where employee was aware of dissolution abatement of claims provision applied even in absence of written notice because employee had actual notice holding that district court may order hearing as remedy for termination of public employee without due process holding that res judicata properly barred claims based on an employers decision to terminate an employee because the termination was not a fresh act of discrimination rather it was the same decision not to allow the employee to return to work that the employee had challenged previously holding that notice to the attorney of record constitutes notice to the petitioner holding that a notice recommending termination of an employee to the board without notice to the employee of employees right to attend and dispute the claims violated due process