Asami's stepfather had two wooden legs. Asami likes to cut off her boyfriends' feet. She gives a similar speech about the razor wire to Aoyama to the one she gave her stepfather. Possible conclusion: She desperately wants to be loved, but sees her stepfather in every man she meets.
For those of you familiar with Japanese Culture, Asami becomes even more terrifying. Japan is still a staunchly male-dominated society, in which women are expected to bow to the wishes of men. Asami vivisects this idea with razor wire while giggling like a schoolgirl.
Okay... the guy in the bag. How long has she been hanging onto him? How long did she plan on hanging onto Aoyama in a similar state? And what happened to Bag Man after she hooked up with Aoyama?
It's possible that the bag man is the record company executive who had been missing for the past 18 months.
Also, now that she's dead, how's anyone going to find him (especially given that Aoyama came no closer to finding her address before the climax of the film)? The answer is: they're not. Of course, allowing him to die (even by starvation/thirst) could be Cruel to Be Kind.
But she is not necessarily dead; she talks to Aoyama after her fall down the stairs; this may have been an hallucination, or she may have broken her neck and been paralysed in the fall. Then again, she is alive in another reality (if one interprets the film as a dream), assuming the scene where Aoyama wakes up with Asumi at the hotel is not a flashback or another hallucination.