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A. The law if one placed a food on a flame on Shabbos without fulfilling the required conditions:
If one transgressed and returned a pot on Shabbos to an area which (according to all opinions) is forbidden for one to return there, whether this was done advertently [with prior knowledge of the transgression] or was done inadvertently [such as he did not have knowledge of the transgression], [nevertheless] the food is forbidden until enough time has passed after Shabbos for one to be able to have gotten this benefit from the food.
If the food is fully cooked: However, this only refers to a case that the cooking of the food which was placed on Shabbos caused the food to condense in a way beneficial for the food. However, if it condensed in a way that was damaging to the food then it is permitted to eat even on Shabbos, as he has received no benefit from the transgression.
Other Opinions: [Furthermore] there are opinions which deliberate even when the food that was returned had condensed in a way beneficial for it, if it should be prohibited at all after the fact, if it was done inadvertently, being that the food was already fully cooked [prior to being returned to the fire].
The Final ruling: One may rely on this latter opinion to allow people who the food was not intended to be heated up for, [to eat from it on Shabbos]. However, for [the person himself who returned it to the fire and for] his household members one should not permit [it to be eaten by them], as the food had also been returned to the fire on their behalf.
B. If a gentile placed ones food onto an oven on Shabbos, in a way prohibited for a Jew to do, is the food permitted?
If the food is fully cooked and still warm: The above [prohibition to eat the food when the conditions were not fulfilled] is only referring to when a Jew himself returned the pot [onto the oven]. However if one returned the pot through a gentile, then even if this was done advertently [I.e. one knew of the prohibition to ask him to do so], the food is permitted [to be eaten on Shabbos] even if the cooking of the food made it condense in a way beneficial to it, as long as the food was fully cooked, as in such a case one does not benefit so much [from the further cooking] being that it was already fit to be eaten.
If the food has fully cooled down: However, this [allowance to eat the food] only applies if the food was [still] a little hot prior to it being placed on the fire, and thus was fit to be eaten. However if it was completely cold [prior to the gentile placing it on the fire], and was thus not fit to be eaten [in its current state], then even if the gentile heated it up on his own on behalf of the Jew [without being told to do so by the Jew], then if this was heated in a way that is forbidden (according to all opinions) for a Jew to do have done, and the Jew which owns the food saw the gentile doing this and kept quiet, then since the action of the gentile was of benefit for him, it is forbidden for any person to eat from it even after it has cooled down, until enough time has passed after Shabbos for one to be able to have received this benefit from the food.
If the Jew was unaware of the gentiles actions: However if the Jew which owns the food did not know when the gentile returned the pot that the food was completely cold or [he did] but he did not at all notice the gentile coming to return it [and thus could not have protested against the gentile], then the food is permitted [to be eaten on Shabbos], being that most probably the Jew did not want at all for the gentile to heat up his food after it had become completely cold, and [thus the food remains permitted, as] the gentile does not have the power to prohibit the food of a Jew against his will.
The law if one transgressed and placed food by a fire in a case that there are opinions which permit it to be done: [Furthermore] (even if the Jew commanded the gentile to return it) if he returned it (even the Jew himself) to an area where there are opinions which permit this to be done even initially, such as to place it near an oven that is not swept or covered, or next to a bonfire, food that was completely cooked but has liquid which has completely cooled down, and [by placing it near the fire] it heated up there until it became Yad Soledes, then although [transgressing such a prohibition according to some opinions] makes one liable to bring a Chatas offering (for the Jew) [if the Jew placed the food there], nevertheless, since there are opinions which allow this to be done even initially as is explained in chapter 318, [therefore] one may rely on their words after the fact (to not forbid the food placed on by the gentile, even if the Jew commanded him to do so).
Summary-The law of the food with which one transgressed and placed it by a fire on Shabbos:
1. A Jew placed it there:
· If the food is fully cooked and further cooking is detrimental for the owner:
It may be eaten by all people on Shabbos
· If the food is fully cooked and further cooking is beneficial for the owner:
· If the food was not fully cooked:
The food may not be eaten by anyone on Shabbos, and may be eaten by all immediately after Shabbos. If however the transgressor did so advertently, the food is forever forbidden for him.
In short: A fully cooked food which was returned in a forbidden way is only forbidden if all the following apply:
1. Further cooking is beneficial.
2. Fire was uncovered, or was covered but food has fully cooled down.
2. A gentile placed it there:
· If the Jew commanded him to do so then it is only prohibited if a) the food was not fully cooked, or b) the food was fully cooked but had fully cooled down and was heated in a forbidden way according to all, such as directly over the fire [even if the fire is covered, as opposed to near the fire, in which case some opinions hold even a Jew may heat it]. If it is fully cooked and warm then it is never forbidden even if further cooking of it benefits the owner, and even if the fire was uncovered.
· If the gentile returned the food there on his own accord for the Jews behalf: Then as long as the Jew did not notice what was done, the food is always permitted [if the food was fully cooked].
 Admur 253:24
 Meaning that there were conditions which are required by all which were not fulfilled, such as that the food was not fully cooked, or the flame was not covered, or it was a Tanur oven of back then.
 Vetzaruch Iyun if this waiting of “Kdei Sheyasu” applies if the food was not fully cooked and one thus transgressed the cooking prohibitions, in which case we rule that it is permitted immediately after Shabbos.
 Admur 253:25
 Meaning one asked a gentile to do so for him.
 Such as the gentile placed it on the fire as opposed to near the fire
 Meaning he did not protest against the gentile doing so.
 Meaning the above allowance applies even if the Jew himself placed it there, and certainly if a gentile placed it there based on his command. However, Tzaruch Iyun from Chapter 318:9 that the Alter Rebbe rules that the custom is that if a Jew himself heats up near liquid food which has fully cooled down, that it is prohibited even after the fact. Perhaps however here the Alter Rebbe is mentioning the letter of the law that it is permitted, while there he is mentioning the custom, which is to be stringent.
 However, to place such food on an oven is forbidden according to all being that the food in this case has completely cooled down, and thus would be prohibited after the fact.
 Vetzaruch Iyun regarding guests.