Krdytkyu

The Shadow's Strength Drain attack states:

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. Otherwise, the reduction lasts until the target finishes a short or long rest.

For a character that is in their true form this effect is straight forward, it reduces the strength score of the character's true form.

There is an ambiguity over which form the strength drain will apply to if it is applied to a character that is in some form other than their true form.

The most common way for this to occur is if the character is under the effect of Wild Shape, Shapechange, Polymorph or True Polymorph, as these change the character into another creature.

Let's say a Wild Shaped character is affected by the Strength Drain attack while in their beast form. Does the Strength Drain carry over to their true form when they drop their Wild Shape, or does it only affect the specific instance of Wild Shape?

Similar questions also arise for the Shapechange, Polymorph and True Polymorph spells.

The Strength reduction would likely only affect your beast form

Jeremy Crawford has said this regarding maximum hit point reduction (borrowed from this answer to a question about maximum hit point reduction):

Jonathan Longstaff
^@pukunui81

@JeremyECrawford What happens when a wildshaped druid that has had its HP max reduced reverts back to normal? Does the reduction carry over?

Jeremy Crawford
^{@JeremyECrawford}

Wild Shape—a reduction to hp maximum doesn't carry over from your beast form to your true form or vice versa.

Although they are different effects (strength reduction and maximum hit points reduction), the reasoning for one would apply to the other, given that they are both reductions that end on a long rest. However, I cannot find anything published in their Sage Advice publication to confirm JC's ruling.

Taking from the description of Wild Shape (PHB, pg. 67):

While you are transformed, the following rules apply:

• Your game statistics are replaced by the statistics of the beast, but you retain your alignment, personality, and Intelligence, Wisdom, and Charisma scores.

And:

• When you revert to your normal form, you return to the number of hit points you had before you transformed.

That part only discusses hit points reverting back to what you had before, and doesn't explicitly mention your maximum hit points or ability scores returning back to normal, it is only implies by the "While you are transformed" part at the start of this bullet list. Without anything explicit to go on, applying the same reasoning as JC seems consistent with current hit points, at least.