A reader wrote “Every time I eat garlic, both cooked and raw, I get a LOT of foul smelling gas… I don’t get this from onions for example…Do you have any idea why this is, what it might indicated as far as the microbiome go? I know garlic is rich in inulin…”
Inulin from garlic is well known, as well as from:
- artichokes, garlic, beans, oats, onions and asparagus [ref]
I also recall that garlic has anti-biotic characteristics:
“From Roman antiquity through World War I, garlic poultices were used to prevent wound infections. The famous microbiologist Louis Pasteur performed some of the original work showing that garlic could kill bacteria. In 1916, the British government issued a general plea for the public to supply it with garlic in order to meet wartime needs. Garlic was called Russian penicillin during World War II because, after running out of antibiotics, the Russian government turned to this ancient treatment for its soldiers.
After World War II, Sandoz Pharmaceuticals manufactured a garlic compound for intestinal spasms, and the Van Patten Company produced another for lowering blood pressure.” [NYU]
Going over to PubMed
- Garlic contains sulfur compounds like allicin, ajoene, allylmethyltrisulfide, diallyltrisulfide, diallyldisulphide and others which exhibit various biological properties like antimicrobial, anticancer, antioxidant, immunomodulatory, antiinflammatory, hypoglycemic, and cardiovascular effects.
- ReducesInflammatory bowel disease (IBD) 
- Reduces free-living (Hexamita inflata), and parasitic (Spironucleus vortens and Giardia intestinalis). Spironucleus vortens
- garlic exhibits antibacterial activity against probiotic bifidobacteria. The aim of the current study was to elucidate the mechanism of action of garlic clove extract (GCE) on Bifidobacterium bifidum LMG 11041, B. longum LMG 13197 and B. lactis Bb12  – so do not take garlic with bifidobactra probiotics!
The foul smelling gas is likely release by species of bacteria being killed. Cross referencing species cited above I found that Giardia intestinalis is garlic sensistive and produces foul smelling faeces  as one possibility. Other possibilities include Aerococcus urinae , Strongyloides stercoralis  and likely many more.
A suggestion to discuss with your medical professional would be whether to try increasing dosage (fresh garlic – not capsules etc) and see if the foul smell eventually clears (suggesting that the bacteria has been effectively reduced). It should be discussed with whoever lives with you… you could be a challenge to be around!.