In the 1930s, an antisemitic saying became popular that, whenever someone fell over a stone while walking, someone would say, "A Jew must be buried there!" - referring to the "burden" which Jewish people were supposed to represent even in death. Also, similar to English, the term can refer to a possible problem or issue. At the same time, there is the connotation in such phrases as to "stumble across" something that you find that thing by mistake - an apt allusion to the experience of coming across a Stolperstein on your own.
Konstanz has its own organization to manage the matter and keeps a registry on the persons listed on its stones. You can view the organization's website, along with the registry and a map of the sites of the stones, here: https://stolpersteine-konstanz.de/liste.html.
