During the movie Queen of the Damned, Marius tells Lestat that they cannot consume the last drop of blood of someone, or else they will die too. What exactly happens if a vampire takes the last drop of blood from someone?
In Queen of the Damned, the lore dictates that if someone drinks "the last drop of blood", they will take death - their victim's death - into themselves...
Interview... states that if you drink the blood of the dead there will be a heavy consequence (although not necessarily death)
The two are not necessarily mutually incompatible: Queen... may just be more elegiac and prosaic in the way it articulates its point.
It's very unlikely the idea of "The last drop of blood" is supposed to be literal, but rather interpreted as some form of accommodated murder. If there were literally no blood left in their victim's body, they would exhibit drastically different signs of decay and de-circulation (particularly in the scene where Marius is explaining feeding to Lestat).
Perhaps the "last drop" is just a more flowery way of saying you will drink the blood of the victim once it has died and become a cadaver, and thus incur what befalls Lestat in Interview....
These two films (if not the books) seem to deploy the same idea in slightly different terminology, but despite the ambiguity it could be inferred to be the same point.
In The Vampire Lestat, Magnuson tells this to the newly made Lestat who, true to form, does it anyway. All that happens is that he actually feels the death, and it momentarily stuns him. Not deadly in of itself, but potentially dangerous when feeding in a dark alley or some such place...a bad time to be psychically knocked senseless, so I can see an elder advising a newbie against this.