See also
fastq_mergepairs command
Introduction to paired read merging
If the paired read length is longer than the biological sequence in the construct, then the reads overflow into the sequencing primer and adapter sequences which bind the construct to the flow cell as shown below. I call this a "staggered" pair.
The fastq_mergepairs command discards any "overhangs" at the ends of the reads which do not align to the other read.