F′ plasmid formation occurs due to
F' plasmid formation results from imprecise excision of integrated F factor in Hfr chromosome. F integration involves homologous recombination between plasmid and chromosome IS sequences. When excising, recombination occurs between homologous sites but at incorrect boundaries, looping out plasmid that carries adjacent chromosomal segment flanking oriT. Resulting F' retains tra genes plus chromosomal genes like lac, making larger hybrid plasmid. Upon transfer, recipient becomes partial diploid for those genes. Correct excision regenerates normal F+ and leaves chromosome intact without extra bacterial genes.
Ref: Griffiths et al., Introduction to Genetic Analysis, 12th ed., Chapter 6: F Prime Formation Mechanism