If I remember right, this was a short story or novella. It was published either in the mid-50s, around Asimov's time, or sometime in the early '00. I read a lot of Asimov around then, as well as Analog SFF, so it's possible it was in the magazine.
What I can remember:
There are an increasing number of malnourished, emaciated people being found in parks and alleys, seemingly just showing up. A detective is given the cases. Through the typical police work, he find the identity of the latest victim, an older man, which records indicate should only be in his 20s.
I think now that he has an identity, the detective traces through the man's life, eventually tracking him back to some scientific facility. Here my memory of the story is kind of blank.
By the end of the story, we find out that time travel exists, and they have been sending people back in time. But it turns out that nothing from the past can come back (not even information), so anything the person ate or drank in the past wouldn't come back. Depending on the length of their stay, any nourishment that was incorporated into their bodies didn't come back, and so the trip back basically kills them.
There might have been a scene where one of the scientists, while on a trip to the past, has figured out what is going on, and is trying to get a book/notes/something relevant back to the future to warn them. Or this could be a memory of something else entirely, thus it's not with the description above.