The tumor suppressor p53 is a key player in the control of genomic integrity and homeostasis in connection with p63 and p73, the two other members of the p53 family. Loss of functional p53 leads to the proliferation and survival of mature cells and progenitor or stem cells that accumulate genetic alterations, thus favoring tumorigenesis. p53 loss of function, observed in a wide variety of human tumor types, is frequently caused by missense mutations more frequently found in the DNA binding domain, but can also be due to the expression of a plethora of viral and cellular negative regulators. Human hepatocellular carcinoma (HCC) represents a specific situation, first because the TP53 gene mutations pattern exhibits a “hot spot” rarely found in other tumor types that is linked to Aflatoxin B1 exposure and, second, because many HCCs do not exhibit any TP53 mutation. Here, we provide an overview of the current knowledge about the inhibition of p53 functions by the N-terminal (ΔN) truncated forms of the family, and their role in the emergence and maintenance of pre-malignant cells with stem cell characteristics and in HCC development. We focus in particular on the Nanog-IGF1R-ΔNp73 axis that is associated with stem-like features in HCC cells and that may provide an attractive new therapeutic target and help to develop new biomarkers for HCC risk stratification, as well as preventive strategies.