We are up to Maseches Terumos, chapter 7, mishnah 3. The mishnah lists four cases in which someone who eats Terumah unintentionally, or feeds it to others, pays only the principal and does not add a fifth - because here there is no act of returning chullin that becomes Terumah, but merely a monetary obligation.
"HaMa'achil es banav ketanim":
Someone who feeds Terumah to his young children, who are not yet obligated in mitzvos and are not kohanim. The children have no right to Terumah, and this is comparable to someone who poured the food down the drain or fed it to a goat. The father must therefore pay for what he took, but this is not a case of chullin becoming Terumah, and so no fifth is added. The children too do not pay, because they are minors - both by virtue of the general exemption of minors, and because the verse explicitly excludes them.
"Ve'es avdo, bein gedolim bein ketanim":
Someone who feeds Terumah to his Canaanite slaves, slaves who are not Jewish, whether they are adults or minors - it makes no difference. In both cases the one who fed them must repay the kohen for having taken what was not his, while the slaves themselves pay nothing, even though they are forbidden to eat this Terumah since they are not the slaves of a kohen. But the reason here is entirely different: a Canaanite slave has no independent capacity to acquire money or property, and under ordinary circumstances there is no way for him to have money at all. He therefore has no means of repaying, since he is penniless, and that is his normal state.
There are two exceptional cases that fall outside this rule:
A slave who was freed: From the moment he goes free, if he wishes to receive his atonement, he is required to pay the principal and the fifth.
A slave who has money in his possession: If one were to devise an unusual case in which a person did a favor for a Canaanite slave and gave him money under the appropriate halachic conditions, whereby the money does not become the property of the slave's master but the property of the slave himself, and with it he could pay the principal and the fifth - in such a case the slave could indeed hold money, and would even be required to buy chullin and repay the principal and the fifth in order to receive atonement for having eaten Terumah unintentionally.
"Ha'ochel terumas chutz la'aretz":
This refers to someone who eats Terumah that was separated outside of Eretz Yisrael. As we have learned, produce that grows outside of Eretz Yisrael - in Syria, in Ammon and Moav, in Egypt and in Bavel - is subject to a rabbinic obligation to separate Terumah. However, someone who eats such Terumah unintentionally does not add a fifth: within the framework in which the Sages obligated separating Terumah outside of Eretz Yisrael, they did not impose the additional fifth for eating it unintentionally.
This does not mean that rabbinic Terumah is generally exempt from the principal and the fifth. On the contrary, it is quite possible that in the time of the mishnah all Terumos were only rabbinic, since most of the Jewish people were not in Eretz Yisrael during that period - they had been exiled five hundred years earlier, and most of them did not return. According to many opinions, and apparently including the practical halachah, even in the time of the mishnah the mitzvah of separating Terumah was not Biblical but only rabbinic. Nevertheless, the mishnayos speak of paying the principal and the fifth, because when the Sages obligated separating Terumah on a rabbinic level, they did not relax the obligations of the principal and the fifth for eating it unintentionally. This obligation, however, was not established in the case of Terumah that comes from ma'aser.
"Ve'ochel pachos mikezayis terumah":
The fourth case is someone who himself eats less than a kezayis of Terumah. In the other cases we were dealing with someone who fed others or who destroyed the Terumah, whereas here he himself puts it down his throat. The rule is that someone who eats Terumah unintentionally pays the principal and the fifth, but this obligation depends on there being an act of eating here. And in order for something to be considered an act of eating in halachic terms, it must meet several conditions:
Fit for human consumption: What is eaten must be fit for human consumption, and here that is certainly the case, since we are dealing with Terumah food.
The measure of a kezayis: The eating must involve the required quantity - a kezayis, the volume of an olive, about the size of a small matchbox. For liquids, the measure is a revi'is.
Within kedei achilas peras: The eating must take place within a span of time that makes it a single act of eating. The Sages fixed this as "kedei achilas peras" - the time it takes to eat about half a loaf of bread, which is between two and nine minutes, depending on the various opinions.
Accordingly, if the volume of food he consumed was less than a kezayis, even though it passed through his mouth, this is not eating in halachic terms, and he does not add a fifth. Obviously, if he ate a Terumah fig cake worth five cents, in an amount less than a kezayis, he must return those five cents to the kohen, the value he took from him, but he does not add a fifth, since he did not perform a halachic act of eating.
This is comparable to one who eats less than a kezayis of pork, for which he is not given lashes, since this is not eating in halachic terms. And even though we rule that half a measure is forbidden by Torah law, and it is forbidden to eat half a kezayis of pork, one is not given lashes for this act, because there is no eating here as halachah defines it.
The same applies regarding the time factor: if he ate a kezayis over the course of ten minutes, he has not performed an act of eating and is not liable for principal and a fifth, but only to return the value of what he consumed.
The same is true if he took Terumah grape juice and introduced it into his stomach through a feeding tube, or had it introduced into his bloodstream intravenously. In all these cases it is not called an act of eating, and if he somehow managed to get the Terumah directly into his stomach, he is not obligated to pay principal and a fifth, since this is not considered an act of eating.
The ruling in all these cases:
In all the cases listed - one who feeds his minor children, one who feeds his gentile slave, one who eats Terumah of outside the Land of Israel, and one who eats less than a kezayis - the ruling is "meshalem es hakeren ve'eino meshalem es hachomesh" - he pays the principal but does not pay the fifth. He must return to the kohen the principal that he took from him, just like one who stole his friend's bicycle or broke it, but he does not pay the fifth.
"Vehatashlumin chullin" - the payment remains chullin. If the one who fed others repays the kohen with chullin food, for example, he gave his children a cup of Terumah wine to drink, and now he returns to the kohen a cup of chullin wine, the chullin wine remains chullin and does not become Terumah, even though it was given as payment for Terumah. For this rule, that the payment becomes Terumah, applies only when one pays principal and a fifth.
"Ve'im ratzah kohen limchol, mochel" - and if the kohen wishes to forgive the debt, he may forgive it. Since there is nothing here but a monetary payment, and not a return of chullin that becomes Terumah, the kohen who sustained the loss may forgive it and say: I do not want your money and I do not want your wine, and that suffices.
This differs from the case we learned earlier: one who unwittingly ate a fig of Terumah belonging to a kohen must return a fig of chullin plus a fifth of the value of a fig, and the kohen cannot refuse it. The reason is that the one who ate needs to obtain his atonement, and the Torah obligated him to give principal and a fifth whether or not the kohen wants the value returned to him.
Here, however, we are dealing with nothing more than a monetary repayment. In practice, one who fed his son a fig of the kohen's Terumah can write the kohen a check, and there is no need to give an actual fig. For this reason the kohen may say: I do not want your money and I do not want your repayment, and refuse it, just as a person may refuse a check from someone who broke or stole his bicycle. And if the kohen wishes to forgive and waive the debt owed to him for the taking of his property, he is entitled to do so.
In summary: this Mishnah lists four cases in which one pays the principal alone without a fifth: one who feeds his minor children, one who feeds his Canaanite slave, whether an adult or a minor, one who eats Terumah of outside the Land of Israel, and one who eats less than a kezayis, which is not a halachic act of eating. In all these the payment remains chullin, and since there is nothing here but a monetary obligation, if the kohen wishes to forgive the debt, he may forgive it.