Joint DNA molecules are natural by-products of DNA replication and repair. Persistent joint molecules give rise to ultrafine DNA bridges (UFBs) in mitosis, which compromise sister chromatid separation. The DNA translocase PICH (ERCC6L) plays a central role in UFB resolution. To better understand the genetic context rendering cells dependent on PICH, a genome-wide loss-of-function screen was performed to identify the genetic contexts in which cells become dependent on PICH. In addition to genes involved in DNA cohesion, centromere stability and DNA damage repair, we identified the uncharacterized protein C1orf112. We find that C1orf112 interacts with and stabilizes the AAA+ ATPase FIGNL1. Inactivation of either C1orf112 or FIGNL1 resulted in UFB formation, prolonged retention of RAD51 on chromatin, impaired replication fork dynamics, and consequently impaired genome maintenance. Combined, our data reveal that inactivation of C1orf112 or FIGNL1 dysregulates RAD51 dynamics at replication forks, resulting in DNA replication defects, and a dependency on PICH to preserve cell viability.