Alternative cleavage and polyadenylation influence the coding and regulatory potential of mRNAs and where transcription termination occurs. Although widespread, few regulators of this process are known. The Arabidopsis thaliana protein FPA is a rare example of a trans-acting regulator of poly(A) site choice. Analysing fpa mutants therefore provides an opportunity to reveal generic consequences of disrupting this process. We used direct RNA sequencing to quantify shifts in RNA 3' formation in fpa mutants. Here we show that specific chimeric RNAs formed between the exons of otherwise separate genes are a striking consequence of loss of FPA function. We define intergenic read-through transcripts resulting from defective RNA 3' end formation in fpa mutants and detail cryptic splicing and antisense transcription associated with these read-through RNAs. We identify alternative polyadenylation within introns that is sensitive to FPA and show FPA-dependent shifts in IBM1 poly(A) site selection that differ from those recently defined in mutants defective in intragenic heterochromatin and DNA methylation. Finally, we show that defective termination at specific loci in fpa mutants is shared with dicer-like 1 (dcl1) or dcl4 mutants, leading us to develop alternative explanations for some silencing roles of these proteins. We relate our findings to the impact that altered patterns of 3' end formation can have on gene and genome organisation.