פרשת ויקרא תשל"א - אשם

Regarding the laws of a guilt-offering for theft, see the worksheet from 1950.

R. David Hoffman in his Commentary on Leviticus (pp. 151-152):

This verse (Leviticus 5:19) clarifies the difference between the sin-offering and the guilt-offering with precise words. Any sinner sins in two ways: First of all, to himself - and it is his soul's purity which is injured by the sin; and [his soul is] distanced from its closeness to God which is its source, whereas closeness to Him is its goal... Sinners of this type are obligated to bring a sacrifice, the object of which is essentially as a "sin"-offering, meaning for purification... But there are other sins that are, largely, more of a sin towards God and a deprivation of His rights... In such cases where there is a deprivation of God's rights - whether directly or indirectly - a "guilt"-offering is required.

On verse 20:

The previous [cases of] guilt-offerings came as a result of sins through which God was directly deprived of one of His rights. But here, it is speaking about the rights of the neighbor, though which God's rights are indirectly injured.

Rashi on the Mishnah:

S.v. And swore to him: falsely (that he did not steal from him) and confessed (in the end); s.v. he must carry it after him even as far as Media: as there is no atonement for him until he returns it to the actual person from whom he stole it.

Ch. Albeck (Commentary on the Mishnayot):

S.v. He must carry it after him as far as Media: and he is obligated to carry it after him, even if he went to a faraway land.

Tiferet Yisrael:

S.v. He must carry it after him as far as Media: which is far away, and where even silver (money) is not considered to be anything, as it is stated (Isaiah 13:17), "Behold, I stir up Media against them, who do not value silver or desire gold."