As mentioned above, self-employed persons pay Class S PRSI, which only counts towards a pension. There is no entitlement to jobseeker or illness benefit with Class S contributions.
If the former self-employed person is available for work, they can apply for Jobseeker's Allowance, which is means-tested.
If a person is unfit for work and has no entitlement to Illness Benefit, they may be eligible for Supplementary Welfare Allowance (if the illness is short-term) or Disability Allowance (if the illness is long-term). Both schemes are also means-tested.