Is there a rule about such cases? I just can not understand.
Downloading a scammer's files.
The name of the video from YouTube.
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Because scammer's is possessive singular.
Using Indefinite Article: a & an
A common noun in the singular number always requires an article before it. But a plural common noun does not require an article always. A plural common noun can have the article ‘the’ if we want to particularise that noun.
If the sentence were "Downloading scammers' files", you would not use the article because scammers' is possessive plural.
Consider this example:
"Buying food for a dog." You use the article because dog is singular.
"Buying food for dogs." You don't use an article because dogs is plural.
To be more exact:
"Buying a dog's food." You use the article because dog is possessive singular, meaning "Buying food for a dog."
"Buying dogs' food." You don't use the article because dogs' is possessive plural, meaning buying food for many dogs (or just more than one dog).