From what I hear, their marriage seems to be falling apart.
Literal
According-to-what-was-heard, they [possessive-の] marriage [topic-は] breakdown has-been-reaching seems [emphasis-よ].
聞いたところによると is the past-tense variant of 聞くところによると — 'according to what I heard.' 破綻をきたしている means 'has reached a state of collapse.' ~らしい expresses the speaker's inference from evidence, softer than ~そうだ.