18 If someone has a stubborn and rebellious son who will not obey his father and mother, who does not heed them when they discipline him, 19 then his father and his mother shall take hold of him and bring him out to the elders of his town at the gate of that place. 20 They shall say to the elders of his town, “This son of ours is stubborn and rebellious. He will not obey us. He is a glutton and a drunkard.” 21 Then all the men of the town shall stone him to death. So you shall purge the evil from your midst; and all Israel will hear, and be afraid. (Deuteronomy 21:18-21 NRSV)
There’s quite a lot of evidence for this in Jewish tradition:
10 Speak to the Israelites, saying: Anyone of you or your descendants who is unclean through touching a corpse, or is away on a journey, shall still keep the passover to the Lord. 11 In the second month on the fourteenth day, at twilight, they shall keep it; they shall eat it with unleavened bread and bitter herbs. 12 They shall leave none of it until morning, nor break a bone of it; according to all the statute for the passover they shall keep it. 13 But anyone who is clean and is not on a journey, and yet refrains from keeping the passover, shall be cut off from the people for not presenting the Lord’s offering at its appointed time; such a one shall bear the consequences for the sin. (Numbers 9:10-13)
If an alien who resides with you wants to celebrate the passover to the Lord, all his males shall be circumcised; then he may draw near to celebrate it; he shall be regarded as a native of the land. But no uncircumcised person shall eat of it; (Exodus 12:48)
25 The priest shall make atonement for all the congregation of the Israelites, and they shall be forgiven; it was unintentional, and they have brought their offering, an offering by fire to the Lord, and their sin offering before the Lord, for their error. 26 All the congregation of the Israelites shall be forgiven, as well as the aliens residing among them, because the whole people was involved in the error. 27 An individual who sins unintentionally shall present a female goat a year old for a sin offering. 28 And the priest shall make atonement before the Lord for the one who commits an error, when it is unintentional, to make atonement for the person, who then shall be forgiven. 29 For both the native among the Israelites and the alien residing among them—you shall have the same law for anyone who acts in error. 30 But whoever acts high-handedly, whether a native or an alien, affronts the Lord, and shall be cut off from among the people. 31 Because of having despised the word of the Lord and broken his commandment, such a person shall be utterly cut off and bear the guilt. (Numbers 15:30)
Were it not that I feared the wrath of the enemy, lest their adversaries should behave themselves strangely, and lest they should say, Our hand is high, H7311 and the LORD hath not done all this. (Deu 32:27 KJV)
But the soul that doeth ought presumptuously, H7311 whether he be born in the land, or a stranger, the same reproacheth the LORD; and that soul shall be cut off from among his people. (Num 15:30 KJV)
And the man who ever should do in pride G5243 to not obey the priest standing beside to officiate in the name of the lord your God, or the judge who ever should be in those days, then [2shall die 1that man], and you shall lift away the wicked one from out of Israel. (Deut 17:12)
And the soul who shall do a thing by hand through pride G5243 — of the native born, or of the foreigners — [3God 1this one 2provokes], and [2shall be utterly destroyed 1that soul] from out of its people,(Num 15:30)
11 You must carry out fully the law that they interpret for you or the ruling that they announce to you; do not turn aside from the decision that they announce to you, either to the right or to the left. 12 As for anyone who presumes to disobey the priest appointed to minister there to the Lord your God, or the judge, that person shall die. So you shall purge the evil from Israel. 13 All the people will hear and be afraid, and will not act presumptuously again. (Deut 17:11-13 NRSV)
Ye shall keep the sabbath therefore; for it is holy unto you: every one that defileth it shall surely be put to death: for whosoever doeth any work H4399 therein, that soul shall be cut off from among his people.
Six days may work H4399 be done; but in the seventh is the sabbath of rest, holy to the LORD: whosoever doeth any work H4399 in the sabbath day, he shall surely be put to death.
Six days shall work H4399 be done, but on the seventh day there shall be to you an holy day, a sabbath of rest to the LORD: whosoever doeth work H4399 therein shall be put to death.
One possible explanation to save my theory is that both happen. Not only is the person killed but they are no longer considered an Israelite since working is a purposeful act of breaking the covenant.