In Illumina sequencing by synthesis are DNA fragments amplified by bridge PCR. Each fragment gets an adapter which is complementary to adapters on flow cell surface. ssDNA fragments bind to adapters on flow cell and then PCR begins and from each fragment is created cluster of clones. But what if two different initial fragments are binded so close that created clusters are also so close and consequently in sequencing, base calls from each cluster cannot be distinguished?
What you're describing happens all of the time and the clusters are flagged before fastq files are ever made. For the most part, the base call quality on such clusters is very very low and even if the cluster somehow passes filter by Illumina's software, it's unlikely to survive after trimming or actually get mapped (if one skips trimming).