If an ability has been attacked such as a SHADOW draining strength... how does the character regain points to the damaged ability 

The abilities that does the damage should list the time.  It is almost always till they take a short or long rest.

In addition a Greater Restoration spell will completely restore one stat.

The ability will always say how to remove the penalty - for example, a Shadow’s ability says “the reduction lasts until the target finishes a short or long rest.”  Additionally, spells like Greater Restoration can end conditions like this, unless the ability specifically states that something like Wish is required. 

Seems like the new entry leaves that part out:

Draining Swipe. Melee Attack Roll: +4, reach 5 ft. Hit: 5 (1d6 + 2) Necrotic damage, and the target’s Strength score decreases by 1d4. The target dies if this reduces that score to 0. If a Humanoid is slain by this attack, a Shadow rises from the corpse 1d4 hours later.

Is there another governing document that gives it a time limit in 5.5?

Benefits of the Rest. To start a Long Rest, you must have at least 1 Hit Point. When you finish the rest, you gain the following benefits:

Regain All HP. You regain all lost Hit Points and all spent Hit Point Dice. If your Hit Point maximum was reduced, it returns to normal.

Ability Scores Restored. If any of your ability scores were reduced, they return to normal.

Exhaustion Reduced. If you have the Exhaustion condition, its level decreases by 1.

Special Feature. Some features are recharged by a Long Rest. If you have such a feature, it recharges in the way specified in its description.