The curse is one of turning the soul into a pig or monkey's.
Surah 2:65, “And indeed you knew those amongst you who transgressed in the manner of the Sabbath (ie Saturday). We said to them: “Be you monkeys, despised and rejected. So made this punishment an example to their own and to succeeding generations and a lesson to those who are the believers.”
One Jewish Kabbalist interprets this has a future re-incarnation. Those who refuse to obey the Sabbath have their souls turned into animals and come back down again. This is the curse placed on them. They live a life of an animal for refusing to obey God's command to rest on the Sabbath. Presumably they return back to their human soul form after this.
This may account why Muhammed abandoned the carrying out of the punishment now for Sabbath disobedience.
Surah 16:124, "The Sabbath was only prescribed for those who differed concerning it, and verily, your Lord will judge between them on the Day or Resurrection about that wherein they used to differ.
One Quran correctly states the punishment for Sabbath breaking is only to be carried out on the Day of Resurrection for the "debelievers".
No doubt the Prophet Muhammed abrogated the punishment for Sabbath breaking whilst carrying out the punishments for other offences. It is somewhat of a curious thing that this punishment is not carried out by the Prophet Muhammed. He surely must have come across Jews and others not obeying the Sabbath.