I’m not aware of a single term that describes exactly verbs that display this type of alternation between intransitive subject and transitive direct object, but it is a common feature of many unaccusative verbs in English (in particular anticausative verbs, and if you used unaccusative verb as a term to refer to this ‘group’ of verbs, you would likely be understood.
In general, a closer unity between the subject of an intransitive verb and the direct object of a transitive verb is a typical feature of ergativity, probably the most common ergative feature to show up in non-ergative languages (like English). In ergative languages, however, this relationship is the norm and is usually displayed by all verbs.
In English, the difference between an unaccusative verb and an ergative verb is the verb’s valency: unaccusative verbs are intransitive, while ergative verbs by definition are transitive. Close, for example, is both an unaccusative and an ergative verb: in your first example it is unaccusative (the subject is non-volitional and not actively responsible for the action), while in your second example it is ergative (a regular transitive verb with a volitional subject and non-volition object, but one that corresponds to an unaccusative intransitive).
(Some people—and the Wikipedia article on ergative verbs—categorise unaccusatives as a subcategory of ergative verbs; there’s nothing particularly wrong with this, except it leaves you without a word specifically for the transitive half of an unaccusative–ergative pair.)