"With the new emphasis on Gulag as the means of concentrating cheap labor, new camps were then constructed throughout the Soviet sphere of influence, wherever the economic task at hand dictated their existence (or was designed specifically to avail itself of them, such as the White Sea-Baltic Canal or the Baikal Amur Mainline), including facilities in big cities — parts of the famous Moscow Metro and the Moscow State University new campus were built by forced labor. Many more projects during the rapid industrialization of the 1930s, war-time and post-war periods were fulfilled on the backs of convicts. The activity of Gulag camps spanned a wide cross-section of Soviet industry." [1]
If you try and dig around a bit, there is no connection between construction of Moscow metro and the Gulag system. None whatsoever. Construction had its share of issues, most notably with work safety, but forced labor wasn't a part of it.
"It is easy to misjudge the Gulag’s contribution because its more lasting monuments—the Moscow metro, the Moscow University, and the Norilsk Nickel Combinat—are what remain. Forgotten are the “roads to nowhere,” long fallen into the decay that is not unique to Gulag projects. The countries of the former Soviet Union are
cemeteries of failed construction projects, which would never have been started if project analysis had not been distorted by the absence of market pricing in the national economy and by the country’s isolation from international markets. Many such projects came into being merely because of fleeting political considerations." [1]
[1] https://en.wikipedia.org/wiki/Gulag