This is actually kinda self-answering, since an ability check being raw specifically means that there are no applicable proficiencies. One of the traps here, is the common shorthand of only referring to the skill proficiency of a roll, but this isn't how they're defined by the rules. An ability check is tied to an ability first, and often has a possibility of letting you add your proficiency. You always add your ability modifier and if you have the applicable proficiency, you add your proficiency modifier. (Skills aren't the only option here either, for example tools and vehicle proficiencies are used this way.)
I think the example actually gives the most clarity:
For example, if a character attempts to climb up a dangerous cliff, the DM might ask for a Strength (Athletics) check. If the character is proficient in Athletics, the character's proficiency bonus is added to the Strength check. If the character lacks that proficiency, he or she just makes a Strength check.
Working with that example: If the DM instead decides Athletics isn't applicable, they'd instead just call for a Strength check. Trimming down the example:
For example, if a character attempts to climb up a dangerous cliff, the DM might ask for a Strength check. The character makes a Strength check.
There are minor exceptions to this, most notably Jack of All Trades with adds half your proficiency bonus to any ability check which don't already use it. And there's a general application of this, as initiative rolls are a Dexterity check.