The COVID 19 pandemic unemployment payment was introduced as an emergency measure to meet the surge in unemployment which resulted from the effects of the Coronavirus pandemic. For self-employed people, they must have experienced a collapse of income and be available to take up other full-time work if it was available to them in order to qualify.
If the person's sole source of income came from rental income and it has now ceased completely, rather than being deferred, they may be eligible for the COVID 19 pandemic unemployment payment provided that they satisfy the other qualifying conditions. If they have other sources of income which they continue to receive they may not qualify. Each case would have to be considered on its own merit before a definite position could be provided.
If a person does not qualify for this payment and they are experiencing financial hardship, they may be eligible for other supports under the supplementary welfare allowance scheme.
I trust that this clarifies the matter.