Was it just me or was there an episode where Punky Brewster gets kidnapped or runs away or something? I don't know if I was just dreamming this or if it was a real episode.

I havent seen any episode like that. But there is one similar to it, where she runs away. Ill have to dig up the episode.

there was an episode involving a kidnapping. i also believe it had something to do with a grocery store, but i am not sure. of course, i could be thinking of another early sitcom.

you might be thinking of an episode of Different Strokes.

There was never a kidnapping.

There was no kidnapping episode, but there was an episode where Punky ran away, because she did not want to get in the way of Henry getting married again (if I remember correctly, it's been years since I saw that show!)