Is it permissible for a person who owns a thousand heads of sheep to write in an official state document, "I have no income," in order to receive a salary designated for those over sixty who have no income?

What you asked about has two cases:

1. First Case: If the state does not grant this salary except to the disabled, the unemployed, or those who have no source of livelihood, then it is not permissible for a person to take it if they do not meet these criteria. This is because the permissibility of the money is conditioned upon the availability of these characteristics. Lying or cheating to obtain it while not being eligible adds to the sin of consuming wealth unjustly, these burdens, as Allah Almighty says: [And do not consume your properties among yourselves wrongfully], and the Prophet, peace and blessings be upon him, said: "Whoever cheats is not one of us," and he cursed the briber and the bribed. 2. Second Case: If the state grants this salary to those who do not have a salary, even if they have another source of livelihood, then there is no harm for the person to benefit from it because they have not violated the conditions. However, this case is rarely found.