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.
By using Switcheroo to hand your opponent a Blightbeetle, you weaponize its static ability to shut down the very mechanic designed to balance persist and undying—effectively preventing your creatures from ever accumulating +1/+1 counters. With this defensive dampener safely on the other side of the table, Shilgengar, Sire of Famine can repeatedly sacrifice your creatures to fuel its ability, generating a steady stream of Blood tokens. Because the creatures return without the counter that would normally lock them out of coming back again, the loop can continue endlessly to rack up infinite death and sacrifice triggers.