Is money taken from a thief who confessed to the theft and signed a blank promissory note, and who paid an amount that was estimated roughly due to the impossibility of an accurate estimation of the stolen goods, lawful or unlawful, especially considering that the thief was a drug addict?

If it is established to you or you strongly believe that the stolen items are equal to or exceed 4000 dinars, there is no harm in you demanding that amount, because rulings are based on certainty or strong presumption. And since the thief confessed to the theft but denied the value of the stolen items, he must swear that he did not steal this value. If he swears, he is to be believed regarding what he estimated, and the remaining amount is to be returned to him, based on the saying of the Prophet (peace be upon him): "The burden of proof is on the claimant, and the oath is on the defendant." It is preferable to refer the matter to the judiciary or arbitration by experts to estimate the value of the stolen items.