Activate Shilgengar by sacrificing the undying creature.
When the undying creature dies, its undying ability triggers, returning itself from your graveyard to the battlefield without a +1/+1 counter on it due to Blightbeetle.
Resolve the Shilgengar ability.
Repeat from step 2.
This wicked loop relies on Harmless Offering to saddle an opponent with Blightbeetle, whose static ability prevents your opponents' creatures from ever receiving +1/+1 counters. With this defensive dampener on their side of the board, your undying creature can continually cycle between the battlefield and the graveyard without ever getting stuck with the counter that would normally shut undying down. Shilgengar, Sire of Famine orchestrates the engine by sacrificing that creature to produce a Blood token, letting the creature return endlessly to fuel infinite sacrifice, death, and entry triggers.