Self employed people do have rights to social welfare, albeit that they are fewer than employees. Self employed people also pay less social insurance than employed people.
Your suggestion is unlikely to be considered genuine employment, but if it were, then the employer would be paying employers PRSI, on top of the employees contribution to PRSI.
Alternatively self employed people could insure themselves with their profit, and would not need to engage in contrived schemes to try and get round the current system.
There is a strong argument however that self employed people should be brought further into the compulsory state insurance scheme, but expect higher contributions than the 4% self employed people pay at the minute if this is to happen.