A retained stone of any sort can be the nidus for recurrent/chronic
renal infection. The most common sort of stone would be CaOx
(wheddellite/whewellite). Anecdotally (not to be confused with a data),
I've passed wheddellite/whewellite/apatite stones associated with my
chronic renal infection, and that was the composition of the stone
removed from the lower pole of my left kidney (ouch). Apatite usually
forms in a pH of 7.3 or higher, but can form in the presence of a
prolonged infection in lower pHs. CaOx stones usually form in low pHs of
5.5 or under, though hypercalciuria and hyperoxaluria can promote stone
formation in higher pHs.

The stones themselves may not cause the infection, but the surface of
the stones are irregular enough for bacteria to 'hide' in and even
though antibiotics are used, the infection is never completely
erradicated. Additionally, there have been some studies linking
nanobacteria to the formation of CaOx and apatite stones.

Struvite stones, which often form 'staghorn' formations, are almost
always caused by infections. They have a different composition than CaOx
or apatite stones, tend to form quickly, and are quite dangerous.

If this is not qiuite more than you ever wanted to know about kidney
stones, just ask!