I'm trying to understand this concept. I've Googled around and could't find any straightforward answers. I don't need too many details, just the explanation that's given in the Gemara (I understand this is derived from the Gemara). Can somebody provide the types of situations this applies to. I'm sorry for typing the way I am, I just heard of this concept and can't get to any books to go deeper into it (as I am on a summer vacation).
here is something I wrote on the subject -- I hope it gives a basis and provides avenues for future investigation.
Kam lei b’deraba minei – During the commission of an aveirah, an individual may invoke more than one penalty. Should he have to be subject to more than one or not? In many situations, the gemara holds kam lei – the transgressor stays subject only to the worse/worst of the punishments. He is not required to be subject to two penalties if both came about by the exact same actions. The gemara in chullin 81b brings up the case of someone who is liable for avodah zarah through his slaughtering, and thus deserves death; he can not also be held liable for oto v’et b’no (slaughtering a mother and offspring on the same day). The worse punishment, killing, is enough. Gittin 52b also comes to this conclusion regarding the mixing of foodstuff.
However, this concept of double liability becomes more clouded when the issues of shogeg and meizid, and the idea of physical punishment versus karet or monetary payment are mixed in. Rav Meir, on ketuvot 33b is of the opinion that a person can receive 2 punishments simultaneously as long as the stricter one is not the death penalty. Lashes can be imposed along with monetary repayment or fine. On 34b-35a the question arises surrounding the aveirah done b’shogeg. If it would have received a certain level of punishment if done b’meizid, does it still need a fine imposed in the shogeg case? And what level of meizid punishment must be hanging over the head of the b’meizid to exempt the shogeg? (Rebbi Yochanan and reish lakish’s argument). When the more severe of the two punishments is karet (according to the machloket on Shavuot 33a, pesachim 29a and ketuvot 30a) Rebbi Nechunya ben Hakanah says that the transgressor is exempt from the lesser penalty but the chachomim say he is still liable. The mishna on bava kama 70a which makes one who steals and slaughters an animal on yom kippur liable to pay tashlumin seems which accords with the opinion of the chachomim – he is not exempt because the greater punishment is karet (rashi).
The rambam’s p’sak is that someone who does an aveirah b’shogeg for which he would be held to mitat beit din and tashlumin, does not pay, and an aveirah for which one receives malkot and tashlumin, the pealty is one or the other depending on the situation (hilchot geneiva 3:1, citing hilchot na’arah 1:13). However (halacha 2), if one were to be liable for mita and then afterwards malkot (or vice versa), that is, that the two punishments are not incurred simultaneously, both must be levied (such as a geneivah on Shabbat which occurs in a private reshut and then later the ganav goes to another reshut and loses the chefetz, he must pay for the item and also be responsible for hotza’ah on Shabbat). This argument is brought down on ketuvot 31a where there is also a discussion of the many events which all contribute to one action and whether all the events become “simultaneous” because they all contribute to the one end result.
In essence, the idea is this:
If a person does one act, and with that one act incurs two different kinds of penalties, we only apply the stricter one. So if a person (for example) borrows a cow and then slaughters it on Shabbos, he incurs two penalties: monetary restitution to the owner of the cow, and the death penalty for violating Shabbos. In this case, Beis Din only applies the stricter punishement, death, and the lesser one, the money, is waived.
Again, there are other details and complexities, but this is the general idea.
קים ליה בדרבה מיניה is used when someone commits two crimes at once. It is learned from the case in the beginning of Mishpatim which says that if two men fight each other and they hit a pregnant woman by accident, then if there is no fatality (i.e. death), the one who hit the woman will be fined. The Gemara makes a diyuk: If there is no fatality, he will be fined; but if there is a fatality, he won't be fined. This is because he is getting a greater punishment: Galus (for accidental murder).
This is not comparable of another rule we have, "kedei rish'aso," which teaches that we only lash someone for one rish'ah (wickedness) and not for two (Makos 4b), and therefore someone who is lashed doesn't also pay money. It is not comparable because kim leih bederabah mineih concerns money and "kedei rish'aso" concerns money and lashes, so we need both pesukim.
Sources: Tosafos, Bava Kama 4a, d"h kir'i; Maharam there