Tar can go bad in the practical sense even if it does not rot like food. Bad storage can make it lumpy, contaminated, overly thick, skinned, separated, or unsuitable for the job.
Tar is not a normal perishable material. Bacteria and mould are not usually the main issue in a sealed tin of tar. The more common problems are physical and chemical changes: evaporation of lighter parts, oxidation at the surface, contamination from dirty brushes, and changes caused by repeated heating or freezing.
A tar that has gone bad may be hard to stir, stringy, gritty, crusted, or unexpectedly thin. It may smell different from a fresh tin, although smell alone is not a reliable safety test. Some old products also become hard to identify, especially if the original label is damaged or missing.
The risk is greater with blended products than with simple traditional tar. A tin sold as roofing tar, bitumen mastic, or wood treatment may contain additives that age differently from the tar fraction itself. That means old product labels and safety sheets matter.
In practical terms, tar has gone bad when it no longer behaves predictably for its intended use. A questionable tin might be acceptable for a rough outdoor test board, but not for a roof, boat, historic surface, animal-related use, or anything where failure would be expensive or unsafe.