Single-stranded DNA-binding serine protease that mediates the proteolytic cleavage of covalent DNA-protein cross-links (DPCs) during DNA synthesis, thereby playing a key role in maintaining genomic integrity (PubMed:32165630). DPCs are highly toxic DNA lesions that interfere with essential chromatin transactions, such as replication and transcription, and which are induced by reactive agents, such as UV light or formaldehyde (PubMed:32165630). Protects replication fork from stalling by removing DPCs, such as covalently trapped topoisomerase 1 (TOP1) adducts on DNA lesion, or poly(ADP-ribose) polymerase 1 (PARP1)- DNA complexes trapped by PARP inhibitors (PubMed:32165630). Required for PCNA loading on replication sites (PubMed:24561620). Promotes S- phase entry and DNA synthesis (PubMed:24561620). Also acts as a restriction factor for some viruses including SV40 polyomavirus and vaccinia virus (PubMed:23093934, PubMed:37607234). Mechanistically, affects nuclear barrier function during viral replication by mediating the disruption of the nuclear pore complex (NPC) via its protease activity (PubMed:33369867, PubMed:37607234). In turn, interacts with vaccinia virus DNA-binding protein OPG079 in the cytoplasm and promotes its degradation without the need of its protease activity but through autophagy (PubMed:37607234). {ECO:0000269|PubMed:24561620, ECO:0000269|PubMed:32165630, ECO:0000269|PubMed:37607234}. This is the function of FAM111A (FAM111 trypsin like peptidase A, Ensembl gene identifier ENSG00000166801).