I don't know if this is the same with all Catholic cemeteries, but the one here in Spokane recently provided free burial for several dead persons whose bodies have been unclaimed from the coroner's office--some for several years. The cemetery took it upon themselves to take care of those that no one else would. I seem to recall that they also provided a headstone. Many cemeteries are private enterprises, so of course would not provide a free service such as a headstone, but the Catholic cemeteries, I think, run in conjunction with the Church, and thus can provide for services that private places would not.