The human dermal fibroblasts can go through 12-15 population doublings. The life span of a cell line can be plotted as the cumulative PDLs versus time in culture. You can subculture the cells until the cell line reaches senescence i.e., there is no change in PDL from one subculture to the next. Senescent cells do not proliferate. Instead, they will change shape and become larger. This is an indication that you can no longer use these cells for your experiments.
When subcultured, these cells are more prone to significant changes with increasing passage as they adapt to in vitro culture. This means that the population doubling number should be carefully recorded. As far as I know human foreskin cells are capable of a few additional doublings before the onset of senescence.
Passage number of frozen cells does not become zero. Whenever a frozen vial is purchased, the passage number is provided on the vial, or whenever you freeze mammalian cells in liquid nitrogen you have to record the passage number.