I would suggest that a second, equally valid interpretation to the splitting of 'black pudding' is that the actions of slashing and piercing weapons works to divide the matter into two halves of the original. That is, that the 'half hp of original creature' becomes the max hp for each halve.
This redistribution of matter, where 10hp is the minimum hp required to form a coherent whole, is different from the reduction in hp until it hits this minimum state of maximum integrity.
In descriptive terms, once a part is reduced below 10hp, parts of the matter become inert. Hence, healing the creature would likely only serve to bring it back to its maximum segment hp - that of 10hp at the lowest.
A little off topic but I would also suggest that a healing could also be used to bring two coherent wholes into a single whole of double the hp, presuming that the original creature could in fact do so - otherwise it would take a greater healing spell capable of healing more permanent injuries (or regeneration) to do it.