If a persist creature is used, it does not have a -1/-1 counter on it.
Otherwise, if an undying creature is used, it does not have a +1/+1 counter on it.
Fallen Ideal attached to a creature you control other than the persist or undying creature.
Steps
Activate
Fallen Ideal by sacrificing the persist or undying creature.
When the creature dies, its persist or undying ability triggers, returning it from your graveyard to the battlefield without a -1/-1 counter or a +1/+1 counter on it due to
Solemnity.
Resolve the
Fallen Ideal ability, giving the creature it is attached to +2/+1 until end of turn.
Repeat.
Results
Infinite LTB.
Infinite ETB.
Infinite sacrifice triggers.
Infinite death triggers.
Infinite power and toughness for a creature until end of turn.