ME, ICC and HLR/AuC are 3G, BSS and VLR/SGSN are 2G. This applies when a 3G subscriber roams into a 2G network - a very common case as networks will introduce 3G technology at different times or not at all.
Upon request by a 2G VLR/SGSN the 3G HLR/AuC produces 2G triplets RAND, RES, Kc out of 3G quintets RAND, XRES, CK, IK, AUTN. It therefore applies conversion function c2 to generate RES from XRES and conversion function c3 to generate Kc from CK and IK. RAND is left unchanged and AUTN is discarded. The 2G triplet is then sent to the VLR/SGSN. Between the VLR/SGSN and the USIM 2G AKA is executed, i.e. using RAND in the request and SRES in the response. No service with a 3G single mode ME.
To handle 2G AKA, the USIM must be capable to accept a request with RAND and return a response with SRES and Kc. The support of the virtual 2G mode is indicated by service no. 38 in the USIM Service Table. Since a 2G BSS is involved, service no. 27 is also necessary. In case the USIM does not support services no. 27 and no. 38, network access is not possible.