What is the absolute minimum XTZ an address has to own to be able to delegate and receive rewards? Even if this is just a theoretical number and not economically feasible. Assuming the wallet can pay for the transaction fee which is required to set up the initial delegation and at some point send the funds back to the tz1 address.
The smallest unit of measure for XTZ is the mutez. 1,000,000 mutez = 1 XTZ. So you should be able to delegate this amount net of transaction fees.
0,000001 xtz plus the transaction fee. so at least you should delegate 0,000001 xtz more than the transaction fee.