The (almost) zero basis scenario can be problematic in terms of gifting stock. However, that issue presumes the would-be donor will predecease the donee (which does not always happen - "best laid plans").
On the opposite side of this coin, you can also have a scenario where the fair market value on the date of the gift is actually lower than the donor's basis. In that instance, the donee will have to use the FMV on the date of the gift to calculate a loss rather than the original basis.
