Some examples that you can research that might be worthwhile:
Simcity DRM workaround through proxy:
http://patheticreviews.com/2013/06/12/how-to-install-simcity-2013-bypass-drmplay-offline/
Also something worth pointing out is Proxy PSN to download P.T.:
http://wololo.net/2016/04/10/how-to-redownload-p-t-silent-hills/
Generally speaking if it's just a simple check, it's very easy to crack always-online DRM.
I suppose that there could be a RNG based check to make it a bit more difficult but it seems like a small speed bump.
I haven't looked into it, but I would imagine looking into pirating Super Mario Run would be revealing for how Nintendo does always-online DRM.
Then the biggest form of always online DRM is, games as a service. Where games have to connect to a database to retrieve proper data. These require reverse-engineering for the most part and are sometimes referred to as private servers or emulated servers.