The Mishna (69a) teaches that there were various types of people who traveled with Ezra the Scribe from Bavel to Israel at the beginning of the Second Temple period. The people divide into different groups, each of which is limited in who they can marry. Thus, for example, families that were known to reliably be kohanim, levi’im or regular yisra’elim could marry one another, but kohanim could not marry a halal (a child born from a forbidden union between a kohen and a divorcee, for example). A mamzer (someone born from an adulterous or incestuous relationship), a shetuki (literally, someone who is “quiet”) or an asufi (literally, someone who is “gathered in”), can marry one another, but they cannot marry people from families established as kohanim, levi’im or regular yisra’elim. The Mishna explained that a shetuki is someone who knows his mother, but does not know who his father is, and an asufi is someone who was found as a newborn abandoned in the marketplace who does not know his parents.
With regard to establishing someone as an asufi, our Gemara brings the opinion of Rava bar Rav Huna who rules that if there are indications that the child was well cared for and was not abandoned to die (e.g. if the baby had been circumcised, if he had a note attached to him, if he was placed in a position where it was clear that he would be found) then the child should not be deemed an asufi, and can marry like any regular Jewish person.
One of the questions that the rishonim ask is how to reconcile the ruling that placement can determine the child’s status – that if he was found in the public thoroughfare he is deemed an asufi, but if he was placed carefully on the side he is not – with all of the other indications (circumcision, a note, etc.) that save the child from that status. One approach is to say that these indications will help us determine whether being left in the public place was with the intent of having the baby found, or for the purpose of being trampled and killed. Another approach is to say that if the child has been well cared for it indicates to us that the child must have been left in a more secure place and somehow was moved into the street.