Shadows are powerful / feared for their Strength Drain ability:
Strength Drain. Melee Weapon Attack: +4 to hit, reach 5 ft., one creature. Hit: 9 (2d6 + 2) necrotic damage, and the target's Strength score is reduced by 1d4. The target dies if this reduces its Strength to 0. […]
— Monster Manual p. 269
Some creatures resist or are immune to necrotic damage, yet there seems to be no mention of creatures immune to death by strength loss. Logically a lich or shadow-dragon is not immune.
Concerns Ad Absurdum:
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Someone dumps a large bucket of Shadows on a lich. Lich dies.
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Shadowdragon breath kills 100 townspeople. The newly minted (angry) shadows touch-drain this dragon and remove enough strength to kill it.
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Orcus, The Lord of Undead, has a group of highly intelligent and successful shadows. In the Abyss he has a great ceremony where congratulates them all by shaking their shadowy hands. As such, the God of All Undead runs out of strength and is suddenly dead / goes out of existence.
Is any creature immune to [shadowy] Strength Drain?
Also: Previously found a stack-exchange post explaining how shadows can strength-drain ghosts RAW. Cannot find it now.
Best Answer
The reasons ghosts can be affected is because rules-as-written they aren't immune to the strength drain effect, only the necrotic damage. Based on the various discussion threads I've seen, many DMs house-rule that anything immune to necrotic ignores the strength drain effect as well.
Currently, no creature is immune to the strength drain effect.