By this, are you referring to the behavior: "By default, this memory image is written to a file named programname.core in the working directory, provided the terminated process had write permission in the directory[...]" (from https://man.openbsd.org/core.5) ?
Also, do you know if there's a way to obtain a core file from a running process on OpenBSD? I don't see a port of gcore, and (e)gdb on OpenBSD doesn't support the generate-core-file command (it says, "Can't create a corefile").