DANIEL E. answered 03/14/19
Adaptable and Flexible French Tutor - All Levels of Proficiency
Hi Michelle:
C'est pas d'sa faute is just a shortening of ce n'est pas de sa faute (it's not his fault).
The French, like us, will shorten words or expressions in every day conversation. Another example would be c'est pas vrai instead of "ce n'est pas vrai" or "sais pas" instead of je ne sais pas.
I think you can safely assume that it there's an apostrophe between two consonants, e.g. d's (as opposed to a consonant and a vowel l'ecole), it is just a shortening of at least one letter in a word or a series of words.
There is no change in meaning or context. It's just a way of shortening every day conversation usually between people who know each other pretty well. It would be like Americans saying "sup?" instead of what is up?
Hope this helps!