That is something I have often wondered about in terms of a fantasy magic setting. The use of magic to temporarily give corporeal form (similar to a ghost, but not the same as) to a powerfully imagined creature, or schizophrenic personality. EG, "what happens when somebody with multiple personality disorder, uses magic to manifest that alt-persona as a semi-physical entity" at one side of the spectrum (extreme)-- and "I have a VERY VERY profound active imagination, and have created a narrative persona that can persist for short periods independently of myself when so channeled" at the other. (EG, JK Rowling might be able to conjure Harry Potter, having fully contemplated his character, ethos, appearance, etc-- if she had the magical ability to expel her inner conception as a physical aparition.)
Assuming a permanent link with the conjurer, (it actually is seated in the mind of the conjurer, not in the apparition it puppet masters), the "death/destruction" of the conjured form would only temporarily banish the apparition-- it would retain knowledge from each time it has been conjured, and grow more and more sophisticated as a conjured being, approaching the extreme version toward the end (actual multiple personality/latent personality) and may represent entirely different skills and abilities than those of the conjurer. Perhaps even seeking to find ways to free itself from the "prison" of the conjurer's mind. (such as via a soul-stone, or other form of phylectory, to serve as an alternative physical anchor to reside in.)
I have considered this a good long while, as for a time, I had considered creating my own pen and paper game engine that would feature such a basis for conjuration. (Where it would cover everything from a simple illusion or parlor trick-- (think magical ventriloquism) to actual "war summons", like the conjuration of an actual being of existential horror to cause unspeakable destruction on a battlefield-- and everything between.) I had considered that there must be a 'cost' to the complexity and capability of such a summon, such as incapacitation/trance of the summoner while active, or a sliding scale of such deficit, depending on the intensity/realness/independent agency of the summon. For the ventriloquist, very little impairment happens, but the summoned "dummy" does not really have independent agency, and is just a puppet of the imagination of the conjurer. In the case of "I summon my inner daemons to rend you apart", the independent agency of the summoned creatures taxes the mind of the summoner, and they have to relent to the agency of the summon, and are thus unconscious on the floor while it tirades around.
One of the consequences I had envisioned for this, if not properly managed or the discipline not followed with proper care, is the ultimate degeneration of the conjurer into absolute madness, as the mind of the conjurer cannot handle having the many minds active inside it that the more advanced form of this practice would produce with time, leading inexcoribly to the directed effort of either the conjurer or the conjured, to seek removal/scion of the conjured into an external construct, where it would act more like a golem-- and being free of its creator, and imbued with individual agency, rebel against its creator's whims, especially if misused.
I dont think any actual existing source book takes that approach though.
I had considered a few possible mechanics to deal with this, such as dividing the base stats and level of the conjurer with that of how many summons he sustains, and that when they are active, he does not have use of that portion of his stat score-- so that, say-- he has 8 int-- He either conjures and unintelligent construct (ventriloquist dummy), with an int of 0 (because it lacks agency)-- or it is some sliding whole quantity thereof-- with the extreme of "summon has all of the stat score, conjurer gets none-- eg, unconscious or unresponsive" as the other far extreme-- at no time does the conjurer+summon(s) score ever exceed the conjurer's base stat score. Being a conjuration, the "body" of the projection is made of magic, so its effective stats (STR, DEX, et al) need to come from somewhere/have some kind of rational basis based on the magical proficiency of the conjurer, but I never got around to that. Considered having it be level dependent.
I had considered having the strength/power of the conjuration be tied with this very deeply, so that the abilities of the summon have to be tied to the potential present in the conjurer somehow-- such as levels invested in conjuration as a skill tree. This way if the conjurer is only a level 3 of this discipline, the conjured being cannot have more than 3 levels of skills at its disposal, at the maximum, with the number of levels it has access to, tied to how "deeply" the conjurer invested this manifestation of the conjured being. (EG, how much of his base stats he imbued it with when he projected it.) -- a kind of thinking that "a thing can only be as big as the box that contains it" in this case, the ability potential of the conjurer.
Because the conjured entity can become wholly intellectually distinct from that of its creator/conjurer, the kind of relationship it has with the conjurer will determine weather or not allowing a full manifestation (conjurer is basically a barely breathing corpse on the ground with no defensive rolls at all) is "safe" to perform or not. (the summon may prefer nihilistic self-destruction over continued servitude, and seek to destroy the conjurer as soon as it possibly can.) Likewise, if the relationship is very positive, (say, healthy parent+child relations), the conjuration would honestly and earnestly seek to protect the conjurer, as it genuinely loves its parent.
EG, the conjurer may decide it is a good idea to lock himself in the top of a tower, conjure his most powerful summon this way, and be content to lay comatose on his bed behind a locked door way upstairs, while his apparition deals serious chaos downstairs-- the destruction of the summon does not destroy the mind of the summon-- it just banishes it temporarily, causing the conjurer to wake up with a start. With some cooldown, can return to the trance, and manifest the summon again, and again. Keep in mind, the summon is NOT the summoner, it is a projection of some alternative perception or imagined being of the summoner.
The desire to either be free of either "a psychotic daemon of my own making", or to "finally be able to hold my dearest child/sweetest love", would be the impetus for the ultimately impossible to avoid final stage of the condition, where the summon is either banished to an external repository (and possibly destroyed), or given independent permanent agency thereby, severing the link with the conjurer in both cases, and removing any direct will based control over the summon (and vis-versa!)
Not anywhere near ready as a custom profession template, by any means, just sharing that I had done some preliminary thought work into such a thing, in case anyone found it interesting.