Final answer:
A client with end-stage kidney failure and on dialysis is eligible for Medicare, which is the healthcare system providing insurance mainly to those older than sixty-five and individuals with certain disabilities, including those requiring dialysis.
Step-by-step explanation:
The client with end-stage kidney failure and on dialysis is eligible for Medicare. Medicare is the public healthcare system that offers insurance primarily to people over sixty-five years old, but it also provides coverage for individuals with certain disabilities and those with end-stage renal disease requiring dialysis or a kidney transplant. Medicaid, another program, is designed to provide healthcare coverage for low-income individuals and families, and while it does cover a significant portion of nursing home care costs in the U.S., eligibility varies by state and does not specifically target end-stage renal disease.