TYPICAL ERROR The rain having stopped the cricket game was resumed.
CORRECTION The rain having stopped, the cricket game was resumed
EXPLANATION Notice that without the comma, a misreading of the sentence is highly likely. We could easily read the opening phrase as The rain having stopped the cricket game ... Of course, if we did misread the sentence, we would immediately realise our error but such confusion is best avoided - especially when all that is required is the insertion of a comma to show where the absolute phrase ends.
Note that many grammarians avoid using absolute phrases completely because such phrases are a grammatical ‘short-hand’. Grammatically, an absolute phrase is a noun with an attached participial phrase; it is not grammatically attached to the rest of the sentence. Consequently, adverbial clauses make more sense grammatically: e.g. Because the rain had stopped,...
Having said that, if we do use absolute phrases, we should insert commas after them.