Why would Qualcomm drop?
To the extent that ZTE was selling phones in markets that required Qualcomm chips (i.e. for CDMA support) their unsold phones will be sold by someone else, who will buy more chips from Qualcomm.
Qualcomm's big problem is that no one is going to need their chips pretty soon since CDMA is going away. Verizon will be shutting off their 2G/3G networks at the end of next year (they will only activate new phones on their network after June 30th this year if they support LTE) so phones sold next year will probably begin dropping CDMA support and once they do they no longer need Qualcomm. Maybe some still choose them for the SoC, but that will be prime time for Samsung, NVidia, Rockchip etc. to start making inroads into phones sold for the US market (and Intel of course for Apple)
That's the real reason they are dropping, and the layoffs they announced have told the market they know they're going to hurt and are preparing for it.
Biting the hand that feeds IT
