Praise be to Allah.
It is permissible to give zakaah to one who does not have enough for his maintenance, even if he has property that he rents out, because this is a case of one who is needy (miskeen) and is mentioned in the verse in which Allah says (interpretation of the meaning): “As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and Al‑Masaakeen (the poor)…” [al-Tawbah 9:60]. Al-Nawawi (may Allah have mercy on him) said: The miskeen (poor, needy) is the one who is able to acquire money or income to meet some of his needs but it is not enough for him. End quote from al-Minhaaj ma‘a Sharhihi Mughni al-Muhtaaj, 4/176.
And Allah tells us in the story of Moosa (peace be upon him) with al-Khidr about the poor and needy people who owned a ship. Allah says (interpretation of the meaning):
“As for the ship, it belonged to Masaakeen (poor people) working in the sea…”
They did not cease to be regarded as miskeen even though they owned a ship.
Based on that, if he has accommodation that he rents out, but what he gets from it is not sufficient for him, it is permissible to give zakaah to him, because he is included in the verse which describes the categories of people to whom zakaah may be given.
Imam Maalik (may Allah have mercy on him) said: If a person has a house and servant and nothing else, he may be given zakaah.
End quote from al-Mudawwanah, 3/221
Al-Nawawi (may Allah have mercy on him) said: If he has property but the income from it is less than is sufficient for him, then he is faqeer or miskeen [poor or needy] so he may be given zakaah to ensure he has sufficient to live on, and he should not be made to sell his property.
End quote from Sharh al-Muhadhdhab, 6/174
In Kashshaaf al-Qinaa‘ (2/273) it says: Imam Ahmad said according to the report of Muhammad ibn al-Hakam: If he has a farm or property that he rents for ten thousand or more, but it is not enough for him, he may receive zakaah. … End quote.
To sum up: If a person has property that he rents out, but what he gets from it is not sufficient for him, it is permissible to give him zakaah to make up what he has, so that it will be sufficient for him and for those on whom he spends, such as his children, wife, father and mother.
And Allah knows best.