Why do loss of function mutations in p53 often lead to mutations in other genes?

The answer to this question would be: p53 normally functions as a tumor suppressor to stop the cell cycle after DNA damage occurs
The function of p53 gene is to stop the cell with damaged DNA to multiply. When the gene works, the cell with DNA damage(mutation) will not multiply, thus there are less damaged cells found. When the p53 gene is damaged, the mutated cell with damaged DNA can multiply so it can be found more.