Evaluate Safety and Biological Activity of ATYR1940 in Participants With Limb Girdle Muscular Dystrophy 2B (LGMD2B) and Facioscapulohumeral Muscular Dystrophy (FSHD)

Inclusion Criteria: * Provided informed consent. * Investigator's opinion, participant is willing and able to complete all study procedures and comply with the study visit schedule. Participant with LGMD2B: * Established, genetically confirmed diagnosis of LGMD2B. * Either the presence of a short tau inversion recovery (STIR) positive muscle on lower extremity skeletal muscle magnetic resonance imaging (MRI), or, if no STIR positive muscles, meets muscle biomarker criteria. Participant with FSHD: * Established, genetically confirmed diagnosis of FSHD. * The presence of a STIR positive muscle on lower extremity skeletal muscle MRI. Exclusion Criteria: * Currently receiving treatment with an immunomodulatory agent, including targeted biological therapies within the 3 months before baseline; corticosteroids within 3 months before baseline; or high-dose non-steroidal anti-inflammatory agents within 2 weeks before baseline. * Currently receiving curcumin or albuterol; use of a product that putatively enhances muscle growth on a chronic basis within 30 days before baseline; statin treatment initiation or significant adjustment to statin regimen within 3 months before baseline (stable, chronic statin use is permissible). * Use of an investigational product or device within 30 days before baseline. * Evidence of an alternative diagnosis other than LGMD2B or FSHD or a coexisting myopathy or dystrophy, based on prior muscle biopsy or other available investigations. * History of …