(Taken from Senguerdius's General and Special Metaphysics)
The inherence that is of the nature of an accident is commonly distinguished into Actual and Aptitudinal. Actual inherence is the union of an accident with a substance, where the accident actually adheres to the substance as a subject. Aptitudinal inherence is a certain aptitude and potential according to which an accident is apt to adhere to a substance.
The question arises as to which inherence is of the essence of an accident: does aptitudinal suffice, or is actual required? This question does not inquire whether the essence of an accident prescinds from existence. It is clear that the essence of any created being can be prescinded from its existence, and that no creature’s essence implies its existence; thus, accidents sometimes did not exist. However, the question should be understood as asking whether an accident can be given that does not actually inhere in a substance but is only apt to inhere in it? It seems that aptitudinal inherence does not suffice, but actual inherence is required. This is proven first from the very definition of being in a subject: since it is required that an accident cannot exist without the subject in which it is, it is not sufficient for the nature of an accident to be able to adhere to a substance. Furthermore, if aptitudinal inherence sufficed for the notion of an accident, it would follow that an accident could be given that does not actually inhere in a substance, retaining, however, the aptitude to inhere, which would then mean the substance is actually an accident. A substance exists because it subsists by itself, not being in another as in a subject, which would apply to such an accident. Moreover, since substance and accident are distinguished in that a substance subsists by itself while an accident inheres in another, just as substance is required to subsist by itself actually, so for the notion of an accident, it is required to actually inhere in a subject. Nor can it be said for the notion of a substance it suffices to be able to subsist by itself without actually needing to subsist: because from this it would follow that the same thing could simultaneously be a substance and an accident.
This demonstration assumes such a being, such a substance that does not subsist by itself but is apt to subsist by itself; according to the opposite opinion, this being would then be a substance. Meanwhile, it would simultaneously be an accident; if it does not subsist by itself, then it actually inheres in another. To be in a subject and not to be in a subject are contradictorily opposed: to subsist by itself means not to be in a subject. Therefore, if that does not subsist by itself, it actually adheres to a subject. If it actually adheres to a subject, then all the more it can adhere; for to be presupposes the ability to be. It is thus clearly intended that the same thing could simultaneously be a substance and an accident if aptitude sufficed for both: an aptitude to subsist by itself for substance, and an aptitude to adhere for accident. The Philosopher in “Physics” book 1, chapter 7, and “Metaphysics,” book 7 chapters 1 and 13, considers it a great absurdity for an accident to be separable from its subject.
From this, it is deduced that an accident cannot adhere to another accident, which, however, must be carefully understood with a distinction between the principal or ultimate subject, which is also called the first and radical foundation, and the less principal subject. The principal subject of all accidents is substance, but one accident can be the less principal subject of another accident, by means of which another accident adheres to the substance, as material accidents are said to adhere to the substance through quantity. That an accident cannot be the primary subject of another accident is apparent because that very accident, being the subject of another, must adhere to the substance by virtue of being an accident.
Here are the places I believe Senguerdius has in mind:
Physics, Book 1, Chapter 7 (read more: http://classics.mit.edu/Aristotle/physics.1.i.html):
But there are different senses of 'coming to be'. In some cases we do not use the expression 'come to be', but 'come to be so-and-so'. Only substances are said to 'come to be' in the unqualified sense. Now in all cases other than substance it is plain that there must be some subject, namely, that which becomes. For we know that when a thing comes to be of such a quantity or quality or in such a relation, time, or place, a subject is always presupposed, since substance alone is not predicated of another subject, but everything else of substance.
Metaphysics, Book 7, Chapter 1:
The term "being" has several senses, which we have classified in our discussion1 of the number of senses in which terms are used. It denotes first the " what " of a thing, i.e. the individuality; and then the quality or quantity or any other such category. Now of all these senses which "being" has, the primary sense is clearly the "what," which denotes the substance (because when we describe the quality of a particular thing we say that it is "good or bad," and not "five feet high" or "a man"; but when we describe what it is, we say not that it is "white" or "hot" or "five feet high," but that it is "a man" or "a god"), and all other things are said to "be" because they are either quantities or qualities or affections or some other such thing.
Hence one might raise the question whether the terms "to walk" and "to be well" and "to sit" signify each of these things as "being," or not; and similarly in the case of any other such terms; for not one of them by nature has an independent existence or can be separated from its substance. Rather, if anything it is the thing which walks or sits or is well that is existent.The reason why these things are more truly existent is because their subject is something definite; i.e. the substance and the individual, which is clearly implied in a designation of this kind, since apart from it we cannot speak of "the good" or "sitting." Clearly then it is by reason of the substance that each of the things referred to exists.Hence that which is primarily, not in a qualified sense but absolutely, will be substance.
Now "primary" has several meanings; but nevertheless substance is primary in all senses, both in definition and in knowledge and in time. For none of the other categories can exist separately, but substance alone
Metaphysics, Book 7, Chapter 13 (read more http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0052%3Abook%3D7%3Asection%3D1038b):
Again, it is impossible and absurd that the individual or substance, if it is composed of anything, should be composed not of substances nor of the individual, but of a quality; for then non-substance or quality will be prior to substance or the individual. Which is impossible; for neither in formula nor in time nor in generation can the affections of substance be prior to the substance, since then they would be separable.
See also Calvinist Metaphysics and the Eucharist in the Early Seventeenth Century by Giovanni Gellera. And see section 4 here: https://plato.stanford.edu/entries/dietrich-freiberg/#QuidQuid There is a common objection to including actual inherence in the essence of an accident, going back to Thomas’s Quodlibetal questions (“As Avicenna says in his Metaphysics, existence is not included in the definition of any genus or species, because all the particular things in a genus or species share that one definition but the genus or species does not exist with one existence in all of them.”), and summarized by the Lutheran metaphysician Scheibler that: “the essence of an accident cannot be posited in actual inherence. In fact, actual inherence denotes the existence [...] and essence as such prescinds from existence.” Dietrich’s considerations are helpful in responding to this line of argument (and Senguerdius implicitly recognizes such a line of argument at the beginning of the second paragraph of this post, seeing it as a confusion). The argument proceeds as if the objection were that actual inherence, and thus actual existence, is so definitional to an accident's essence that accidents must exist as actually inhering, and thus actually existing in every possible world. But the objection, accurately stated, is that actual inherence is an essential mode of an accident such that in any possible world in which an accident actually exists, it actually inheres. That actual inherence is an essential mode of accidents see especially the four disputations on the power of God by Voetius/John Carre, to which I cannot do justice: https://brandoncorleyschoo.wixsite.com/brandoncorley/post/gisbertus-voetius-select-disputations-translated-by-onkuoh
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