The investigators expect to enroll 15 participants with relapsed or refractory IgM-associated AL amyloidosis onto this Phase II clinical trial. Idelalisib will be self-administered orally at a dose of 100 mg twice daily (may be increased to 150 mg (one tablet) twice daily after 3 months at investigator discretion). Participants will be treated until disease progression, unacceptable toxicity, or decision to withdraw from the trial. Disease evaluations will be performed every three months until disease progression.