Used to work in NonStop/SQL which was fully integrated into NonStop/C, NonStop/C++, NonStop/Cobol, NonStop/Fortran, and probably other languages as well as being fully integrated with NonStop/Guardian, the operating system on which the computers ran.
I think that's probably the closest integration you can get, where the database IS the filesystem of the operating system. It's also a dead end, there's no way to decouple any of the components, the database, the operating system, the hardware, and any software written on it can never be used separately, ported to another environment.
The closest you're going to get on a PC would likely be MS Access, Embarcadero/Borland Delphi being a close second.
After that, you're looking at embedded databases in your application, which can have limited appeal to those creating standalone applications that need a set of hierarchical data that's not easily stored in a simple configuration file and/or needs regular updating as the application runs. Or for people wanting to have a portable version of an application that maintains a snapshot of part of a larger database and maybe synchronises that with the larger database at times when the application can make connection (handy for say a salesman who's often out of reach of the corporate network yet needs sales data for his group of customers, or a doctor in the field who wants patient records but can't connect to the hospital network because there's no network access where he has to go).