Commentors on a recent post here began arguing the side issue of bacterial immortality (derived from the question of whether the last universal common ancestor of all living organisms is extinct or whether it, in some way, is still with us today). Though the argument, as presented in the comments, was largely semantic, the central point was summed up by Don Cox in the statement: "When a cell divides (or multiplies) into two identical cells, you cannot say that one or other is an offshoot". This is a common textbook representation of binary fission as practiced by most bacteria and many eukaryotes*. As with many textbook representations, it is highly likely to be wrong.
*Or most, depending (again) on your choice of semantics. After all, you yourself multiply by binary fission, at least at the internal level.
Any cell, whether bacterial, eukaryote or what have you, is constantly bombarded throughout its life by inimical factors. Toxic substances build up, whether ingested from the outside world or produced as by-products of the cell's own metabolism. DNA and other vital cellular structures become damaged or otherwise functionally altered (for instance, by the process of DNA methylation). As this damage builds up, the cell 'ages' and, if the damage becomes too great, dies. One of the reasons cells multiply in the first place is to counter-act the build-up of these inimical factors. For instance, replication of a chromosome will produce a daughter chromosome in which the damage to the original has been repaired (I'm over-simplifying matters, of course, but you get the idea).
To return to Don's statement above, the crux of the error lies in the belief that the "cell divides... into two identical cells" (emphasis added). But the two resulting cells of binary fission are not necessarily identical if the distribution of the original parent cell's accumulated inimical factors is not even. It may be possible that one cell receives the bulk of the problems while the other cell is left 'clean' (Nyström, 2007). Such uneven division has long been recognised in unicellular organisms such as bakers' yeast Saccharomyces cerevisiae that reproduce by budding, which after all is essentially fission in which the distribution of cytoplasm between the resulting cells is uneven. The budded 'daughter' cell contains little inimical factors when produced while the 'parent' cell retains the bulk. The first record of aging in a bacterium was also in a budding species, Caulobacter crescentis. In Caulobacter, a sessile stalked cell gives rise to a mobile swarmer cell (which will itself eventually develop into a stalked cell). However, each time the stalked cell produces a swarmer cell, it takes longer to produce the next one. It becomes old.
Demonstration of similar aging in Escherichia coli, which produces superficially identical cells through fission, was achieved by Stewart et al. (2005). Rod-shaped E. coli cells multiply by elongating then dividing transversely across the middle so each daughter cell ends up with one of the original cell ends plus one newly produced end. But if we follow the cells to the next generation then one of their daughter cells will have an end that has persisted across at least two divisions while the other will have persisted for only one. One cell is therefore 'older' than the other and Stewart et al. discovered that 'older' cells took longer to grow and reach division than 'younger' cells. Based on the rate at which reproduction of older cells slowed down over successive generations, Stewart et al. calculated that a given cell end would persist for about 100 generations which also matches the rate of aging calculated for Caulobacter stalked cells. Similar aging has also been demonstrated in the fission yeast Schizosaccharomyces pombe, a eukaryote that multiplies by equal binary fission.
As summarised by Nyström (2007), evolutionary modelling has indicated that asymmetric division of aging factors during multiplication may offer a selective advantage. Essentially, the chamces of one rejuvenated cell surviving and reproducing, even at the expense of producing one elderly cell, may outweigh those of two mediocre cells. Whether the aging process demonstrated by Stewart et al. (2005) leads to eventual cell death in nature remains unconfirmed but it does seem a very likely inference.
Nyström, T. 2007. A bacterial kind of aging. PLoS Genetics 3 (12): e224. DOI: 10.1371/journal.pgen.0030224.
Stewart, E. J., R. Madden, G. Paul & F. Taddei. 2005. Aging and death in an organism that reproduces by morphologically symmetric division. PLoS Biology 3 (2): e45. doi:10.1371/journal.pbio.0030045