I am no expert, but if it were me I would empty the drawer. Wipe it down with white vinegar. Allow to air out overnight. Then if I could still smell something, I would put coffee grounds in there or maybe baking soda. I don't know which I would try first. Then I would be sure the garbage goes out nightly and put a lid on the garbage, just in case.

Maybe somebody with actual expertise will answer. Good luck. That is one icky problem.

I would clean it all out and the drawer above it too, and then I wouldnt be putting trash in there anymore I would buy a kitchen type trash can, that is easy to wipe out, and gets emptied whenever it gets full. I have never liked having trash cans under sink, or the trash cabinets, for just that very reason.

I have had my trash in a drawer/cabinet forever and it has never once caused a smell. I take out the garbage daily as a rule. Maybe something nasty leaked accidentally and the OP did not notice until things became rancid.

I like Rita's plan to get rid of the smell. Also check the trash cabinet and clean as needed. You could also try this:

When smelly cabinets don't respond to gentler solutions, try mixing a
solution of 1/2 cup of rubbing alcohol into 1 pint of mineral oil. Wipe
down the insides and outsides of cabinets and drawers to banish the
smell almost immediately. (https://homeguides.sfgate.com/rid-kitchen-cabinets-smells-91161.html)

I keep trash and recyclables in the trash cabinet, but not the garbage. Our garbage, which includes paper towels and tissues, gets tossed in a straight sided stainless steel dog food bowl on the counter and emptied as needed. Sometimes "as needed" can be 3+ times a day (when canning) or maybe every other day when not much is going on. Garbage out in plain sight does not stay there long enough to get smelly, because, eww! Putting things like the foam trays that chicken and fish come in in the trash warrants an extra trip to the outside trash can.

Let us know how it works!

I keep the garbage in a pull-out, and it doesn't stink up anything. So yea - something probably spilled in the drawer and went unnoticed.

Is the wood moldy or rotting?

i would take the drawer out, and scrub the stain with dish soap and baking soda to see if you can lift some of the oil out of the wood/particle board. Allow to completely dry, and then seal it with shellac or something like kilz.

Or, go back to that article I linked above. It also said about the mineral oil and alcohol:

This not only wipes away bad smells but seals the wood to prevent new odors from forming. Unlike paint, this gentler solution preserves cabinets while offering extra protection.

It sounds good.

Is there a dividing panel between the drawer and the pullout beneath? If when you take the drawer out, you can see into the trash, you'll want to get a piece of plywood or something in there to separate them.

Was the house empty for a while. Maybe a mouse died in drawer and left that stain and smell.

I would remove the drawer front and replace the drawer box. There are many places on line that sell drawer boxes. Here's one.

https://www.barkerdoor.com/Custom-Drawer-Boxes-s/76.htm

If you can, remove the drawer, turn it upside down and take a picture that includes a view from the back end of the drawer and post it. It is possible that the drawer bottom can be replaced relatively easily, depending on how the drawer is constructed.

"Was the house empty for a while. Maybe a mouse died in drawer and left that stain and smell."

That's a thought, too -- dead mouse is a terrible smell.

Do you have a disposal in your sink? I have a pull-out trash, and I had a disposal that I needed to replace. During the 10 days or so between when the old low-quality one was removed and the new one put in, I could not believe the difference in how bad my garbage smelled. I mean, it was incredible. I do not compost because I

The actual pull-out itself held the trash? Seems like the whole thing needs to be sanitized. Start by removing the pull out and cleaning every exposed surface inside the cabinet with dish soap/water, then wipe with vinegar, then baking soda/water mix.

i don't know what your first photo is showing but it looks like it needs to be cleaned.

Replace the drawer. It’s gross, like they kept piling onto the trash mound rather than just taking it out. Replace that trash can. Scrub the base cabinet with a peroxide and vinegar combination using a microfiber cloth. Wipe down the residue with a microfiber and clear water.

Trash inserts should never smell, if people just take out the darn trash. If something smelly like fish or meat trimmings needs to be waste, wrap it in a plastic grocery sack and freeze until trash day. You don’t put that in either the inside or outside bin to ferment for days.

Compost, done correctly, does not smell either. No one lets the trimmings pile up indoors. Or, they shouldn’t. Not without having a good stack of browns to add to the greens. If you balance correctly, you can even have a worm bin under your sink and no visitors will ever know.

The black soot like marks looks like mildew. Maybe a cabinet closed up with no air and moisture from garbage? I would clean with bleach air it out with a fan, clean again with bleach, dry out really well then get some glossy paint on the porous wood that's easy to wipe. That is a inside the cabinet view isn't it?.... just looked at pictures again, that's the underside of the pull on trash bin holder I guess.

https://cleaningbusinesstoday.com/blog/hydrogen-peroxide-vinegar-a-disinfecting-duo/

The drawer slot needs a floor.

All the other stuff--cleaning, sealing, frequent emptying, etc.--needs to happen, too, but the drawer is pretty much in the trash cabinet. If the trash cabinet smells, the drawer will too.

Ugh, I am so frustrated on your behalf that this mess is not even your own ooopsie (this is a far cry from something leaked accidentally). Yuk. I would really look into rebuilding those drawers and starting fresh. I am sure a handy person could manage it for little money.

We removed our drawer and trash bin and thoroughly cleaned them. We added apiece of Masonite to fit between the trash and bottom of the drawer and sealed it with silicone. You could sand the drawer and paint it with a cleanable paint or poly coat. I would even try to refinish the trash interior of the cabinet.

I use cheap thin .60 peel and stick tiles under my sinks, nobody sees them. That would probably work. Once you get it cleaned and sealed it shouldn't smell. Maybe a Kiltz sealer would work best. Supposedly some if that stuff even seals cat pee smells, but I don't know how myself.

The drawer bottom doesn't need to be replaced. The 'stain' looks like wood stain or toner overspray from when the cabinets were first finished.

I would sand the bottom of the drawer and the sides & back and give them a couple of coats of unpigmented shellac (BullsEye shellac) to seal in any odors that the raw wood might have absorbed.

And thoroughly clean the inside of the cabinet and drawers with chlorine bleach or a quaternary disinfectant. Allow to dry thoroughly for several days and then coat with shellac. Seal all of the interior wood surfaces of the cabinet with shellac. Including the underside of the countertop if your counters are laminate glued to plywood or particle board.

I suspect that the wood has absorbed a couple of decades worth of trash stink and that, once you get all of it disinfected, dried out and sealed with shellac that the old odors will be history.

Going forward, I would really, really try to find an alternative place for the trash. Or at least be vigilant about removing the trash daily. (I take smelly stuff like fresh meat packaging, tuna cans, etc. directly to the garage trash can and I have a free-standing trash container in the kitchen.)

**ETA You want to use a shellac product to seal odors. Real shellac.

The reason why I think the black 'stain' is overspray is because I can see where it looks like the finisher had set the can of stain on the bottom of the drawer as well as blobs of oopsies from the stain on the drawer back.

Looks like a home made garbage pullout... You may want to go to Rev-A-Shelf and get a new system. I believe they also sell drawer boxes. Remove that, clean up the interior of the cabinet - paint it if need be and install the new pieces. You can also get lids for the garbage ( if the rail on your cabinet is high enough ).

Good luck!

I compost using a plastic ice cream bucket with a snap lid that gets emptied into the compost when it's full. Our trash never smells except on the rare occasions when meat packaging goes in, with those absorbant diaper like pads they use under the meat so you don't see all the water you are buying. :-\

One thought about mineral oil/alcohol treatment: I can believe it may remove odors, as a solvent. However mineral oil (after the alcohol evaporates) will not really 'seal' the wood. In fact organic molecules will prefer to dissolve in it, right out of the air. You would need varnish or shellac, as suggested, as a sealer.

Activated charcoal is another way to absorb odors from cabinets or fridge. The stuff they sell for aquarium filters, in a bulk bag, is probably the cheapest way to get it.