Kitchen cabinets attached directly to stud with no drywall

[Jerry Peck - Codeman]

From what I am envisioning of your description, that the cabinets are built-in and the back of the base cabinet IS the wall covering, that there IS drywall in the space between the base cabinets and the upper cabinets, and that the back of the upper cabinets IS the wall covering, and that there IS drywall in the space above the upper cabinet ... and that the wall is an interior wall and not an exterior wall ... and that this is likely an very old house ... there was nothing in the code prohibiting that, however, with modern cabinets which come in 'boxes' which mount together or pre-custom made sections which are simply attached to the wall - what you describe would be a VERY unusual practice and one which, while maybe not being prohibited by the code would certainly expose a VERY CHEAP builder who would cut each and every corner they could find ...

As you can probably tell, I do not have enough information to make an informed answer so I am throwing ideas out based on what you might have.

If it is a new(er) house, I seriously doubt that would ever pass plan review or inspections.

If an older home with cabinets custom made on the site for that specific home, I can see that happening back in the 1940s and earlier.

[Jerry Peck - Codeman]

Because you are referring only to interior walls which do not separate the living space from the garage or outdoors (you did not answer that part of my questions so I am making the statement presuming this to be the case), the main things I can think of are: a) energy related - air infiltration and exfiltration into an attic above or crawlspace or basement below through unsealed openings; b) fire related - the unsealed openings in a) can also lead to the quicker spread of fire and the current setup does not fully and effectively restrict and separate the room air from the air in the concealed space betweens the studs; c) sanitary - being as the concealed space between the studs is not fully and effectively restricted or separated from the room there is the great likelihood that insects will freely travel back and forth from the room and their concealed hiding spaces leading to contamination of everything the insects crawl on or over; d) other items the more I think about it.

This was done during an unpermitted kitchen remodel.

Can I get a certificate of occupancy on this?

Not where I am located, but you may in some areas which have less stringent building codes and less effective enforcement of those codes - some areas STILL have NO codes and NO enforcement, it is build-it-as-you-will-and-anything-goes, which is not good for the occupants or future owners (not sure if you did this as an occupant or if you are one of those future owners who got stuck with it).

I also thought of another solution that might work. Could 1/4 sheetrock be slipped between the cabinets and the studs?

Very unlikely that would work, and you would not really have any real way to seal all the joints.

Your best solution is to remove the cabinets and back splash, install 1/2" drywall, tape and finish the joints, then reinstall the cabinets and back splashes - keeping in mind that if there is a 'U' or 'L' that the area is now either 1" shorter (for 'U' areas) or 1/2" shorter (for 'L' areas). There is likely one or more trim filler pieces which could be cut narrower to make up for the loss of wall length.