Clearing the parent from the UI using the X (or from python) clears the
parsubstr and set partype back to PAROBJECT.

Using the Clear Parent operator would leave the parsubstr (and thus
parent_bone) untouched even though this operator claims to "clear
parenting relationship completely" (it also removes parent deform
modifiers for example).

So now, also clear parsubstr and set back to PAROBJECT [which is
default].