It happened that after a while the spider dropped the remains of the fly into a place that was clean enough I could retrieve them for examination.
There was an impressive amount of damage!

Stereo pair, crossed eye:

Clearly the process is not as simple as "insert fangs, suck victim dry".
In fact the victim got worked over quite a bit, with multiple puncture wounds into various body cavities that were worth the trouble.
The legs of this subject are pretty much intact, except for gaping holes around the joints where they attach to the thorax. The eyes and abdomen show numerous puncture wounds, as seen here.
--Rik
Technical: Canon T1i camera, Mitutoyo 5X NA 0.14 M Plan Apo at 5X, 86 frames at focus step 0.020 mm. Zerene Stacker, stereo at +-3% in portrait orientation, which is also very close to +-3 degrees, so total 6 degrees of stereo separation. Both the single image and the stereo images were retouched from corresponding Stack Selected of just the front half of the stack, to address "transparent foreground" artifacts mostly around the foreground antenna and proboscis.