He sent me a letter to the effect that the poultry business would go bankrupt sooner or later.
Literal
Poultry-business [topic-は] sooner-or-later bankrupt [probably-だろう] [quotative-という] [possessive-の] gist [possessive-の] letter [object-を] he [topic-は] me [to-に] sent.
A complex multi-clause sentence. ~という旨 ('to the effect that / the gist being') is a formal structure where 旨 ('the gist / main point') receives an embedded quoted clause. 遅かれ早かれ ('sooner or later') is a fixed pair using the old conjectural ~かれ form. よこす ('to send over') is a casual variant of 送る with a slight 'send toward me' directional nuance.