First I'll say that, if you follow the traditionalist approach, go 100% with what Olivia has posted above.
But I have a different outlook relative to cazimi; its probably because of my alchemist connections and studies coupled with my decidedly symbolist outlook relative to astrology. For me, cazimi rescues from any and all debilities and detriments-period!
You will find a high appraisal of cazimi in some of the older (mostly Arabic era) astrological literature, but its symbolic quality is extolled among the alchemists (there is a great deal of "hidden" astrology in the alchemical literature, if you know how to see it) The only time cazimi is lessened in its salutary effects, is if the Sun/cazimi planet is in a pitted degree, and even there the cazimi "shines from its pit" to a significant extent. In addition to this theoretical/philosophical outlook, I (believe) I have seen the reality of this outlook validated (in charts) on numerous occasions-I really believe I am correct in this view of cazimi.
Another point is the issue of Fall. Today (and for at least the past 900 years) the Fall of a planet is considered to be the entire zodiacal sign. This was not always the case. In the Greco/Roman astrological literature (and early Vedic literature as well) the entire sign was NOT considered to be the Fall of the planet: only a couple degrees before and after the exact Fall degree, was considered to be the Fall of the planet; if the planet were in that sign but not in or near the Fall degree, it was NOT considered in Fall, nor, in fact, even in detriment. By the time of Al-Biruni (1058 AD) this subject was STILL not definitely decided. In his "Elements of Astrology", Biruni mentions that there was controversy over the issue of Exaltation and Fall: he stated that some considered only the exact degree and a couple degrees before and after it (as did the Greco/Roman astrologers before them), that others considered the degrees of the sign prior/up to the exact degree as being in Fall (or Exaltation), and that still others believed that the entire sign was the Exaltation or Fall for the planet concerned. By the 12th century (in the West at least) the matter was settled and everyone since then has considered the entire sign the Fall (or Exaltation) of the planet (in Vedic astrology this is not the case; only the specific degree areas of Fall-or Exaltation-are given credit, just as in the old Greco/Roman times)
So, to my mind, these historical considerations add more question to this specific example of a cazimi planet in the sign of its Fall: what would I do? I would see if the Sun/cazimi planet were in or within a couple degrees of the specific Fall degree: if so, then I would downplay the benefit of the cazimi state. If not, however, I would count the cazimi state as a DIGNITY and not consider the Fall to exist, for that planet, at all...
PS
What do I do in practice relative to this Fall (and also Exaltation) matter? In almost all situations I do what everyone else does and consider the entire sign to be the Fall or Exaltation sign, and delineate accordingly. With one exception: regarding Sun in Libra I only regard its Fall within the actual degrees of the Fall; especially do I follow this in natal: I could never accept that ALL Librans have a dejected, Fallen Sun-never made sense to me, so I apply the 5 degree-area (2 before, exact and 2 following) of the specific Fall degree of the Sun in these nativities. And I often question to myself-can the Sun ever really be in Fall? After all its not a planet nor a satellite=it is a star, and many of us believe the stars to be "above" such mundane modifying forces as dignity and debility-that often bothers me, with the Sun, but I still follow the generally accepted attitude and practice re to the Sun and its "Fall"...