I'm a bit confused by what "on their own" means,

Question

especially when, in an example, "le jour suivant" isn't used on its own. I read the Q&A, and I'm still confused.  Which sentence structures are correct for which phrases?

Accepted Answer

Bonjour Susan,

"On their own" here means with no direct complement attached to it.
For example, in "le jour suivant, j'ai fait ça" , the expression is used on its own, as it is then separated from the rest on the sentence by a comma, so it is used on its own.
Whereas in "le jour suivant son retour, j'ai fait ça", the expression is completed by "son retour" (i.e. the day following what? his return), therefore it is not used on its own here.

I hope that helps clarify it!
À bientôt !

Answer

Merci, Aurélie, for clarifying. 
Unsurprisingly, there would seem to be many ways to skin this particular cat.  I would be most interested in which ways are used most often in conversational and informal (i.e., non-academic) written French. 
I'm beginning to envy La Bourgeois Gentilhomme for speaking prose.

Answer

Yes I agree and the answer by Aurélie does not answer the point. The example in the lesson is "Il a été relâché le jour suivant son arrestation." so what is meant by "on their own?