OK, I looked back to the 1978 NEC, and that is the same as the 2017 NEC regarding Table 310.15 (B)(7). #2 Cu is 125 amps for resi, single phase service.
Based on what you said, it sounds like someone did a little 'rube goldberg'.
As to the solar, a 'line tap' is used when in lieu of the solar backfed cb when buss space is not available.
