Are there certain biochemical processes that would normally cause a cell to self-destruct but if the cell being tested has apoptosis mechanisms that have malfunctioned or been 'turned off' the cell will not 'malfunction' because of the induced process ? Are there such biochemical processes that could indirectly indicate which cells have no functioning apoptosis mechanisms? If so would this be a possible test for cancerous cells?
In some cases yes — when there is a mutation in apoptotic regulators such as Bcl2 family of proteins. In other cases it is difficult to identify and only identification is that those cells are growing rapidly; in other words failure to undergo apoptosis is not the cause but the effect of the cancerous transformation (as in case of p53, Ras, Myc mutations etc).