Involuntary Cooldown — ruling 1

If a tapped permanent with a stun counter on it would become untapped, a stun counter will be removed from it instead. This is a replacement effect.

Involuntary Cooldown — ruling 2

Stun counters replace untapping for any reason, including players untapping tapped permanents during their untap steps.

Involuntary Cooldown — ruling 3

If a permanent has more than one stun counter on it, only one will be removed each time it would become untapped.

Involuntary Cooldown — ruling 4

Abilities that trigger when a permanent "becomes untapped" won't trigger if a stun counter is removed instead.

Involuntary Cooldown — ruling 5

If untapping a permanent is part of a cost (such as that of Halo Fountain's first ability), you may pay that cost by "untapping" a tapped permanent with a stun counter on it. The stun counter will be removed and the creature will remain tapped. However, the cost will still be paid.

Involuntary Cooldown — ruling 6

On the other hand, if untapping multiple permanents is part of a cost (such as that of Halo Fountain's last two abilities), you can't "untap" the same permanent more than once to pay that cost.

Involuntary Cooldown — ruling 7

Stun counters exist independently of the effects that created them. If a permanent has no stun counters on it, it will untap as normal.

Involuntary Cooldown — ruling 8

Stun counters are not keyword counters, and they don't cause the permanents they're on to gain any abilities. They won't be affected by effects that cause permanents to lose all abilities.

Involuntary Cooldown : règles, fonctionnement et interactions (MTG)

Involuntary Cooldown is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Tap up to two target artifacts and/or creatures. Put two stun counters on each of them. (If a permanent with a stun counter would become untapped, remove one from it instead.)

How it works : Involuntary Cooldown

Original English text — Wizards of the Coast / Scryfall

#1October 14, 2022· Wizards of the Coast
If a tapped permanent with a stun counter on it would become untapped, a stun counter will be removed from it instead. This is a replacement effect.
No other card is named in this ruling.
#2October 14, 2022· Wizards of the Coast
Stun counters replace untapping for any reason, including players untapping tapped permanents during their untap steps.
No other card is named in this ruling.
#3October 14, 2022· Wizards of the Coast
If a permanent has more than one stun counter on it, only one will be removed each time it would become untapped.
No other card is named in this ruling.
#4October 14, 2022· Wizards of the Coast
Abilities that trigger when a permanent "becomes untapped" won't trigger if a stun counter is removed instead.
No other card is named in this ruling.
#5October 14, 2022· Wizards of the Coast
If untapping a permanent is part of a cost (such as that of Halo Fountain's first ability), you may pay that cost by "untapping" a tapped permanent with a stun counter on it. The stun counter will be removed and the creature will remain tapped. However, the cost will still be paid.
No other card is named in this ruling.
#6October 14, 2022· Wizards of the Coast
On the other hand, if untapping multiple permanents is part of a cost (such as that of Halo Fountain's last two abilities), you can't "untap" the same permanent more than once to pay that cost.
No other card is named in this ruling.
#7October 14, 2022· Wizards of the Coast
Stun counters exist independently of the effects that created them. If a permanent has no stun counters on it, it will untap as normal.
No other card is named in this ruling.
#8October 14, 2022· Wizards of the Coast
Stun counters are not keyword counters, and they don't cause the permanents they're on to gain any abilities. They won't be affected by effects that cause permanents to lose all abilities.
No other card is named in this ruling.