The BlackBerry brand
It's possible that someone might want to use the BlackBerry brand for their own messaging-oriented devices, to appeal to those who like physical keyboards on smartphones and just want a device for email and social messaging. There are Android devices that have comparable keyboards but are gunked up with apps, so transplanting the BlackBerry brand to them would be problematic. Likewise, Windows Phone 7 is very much oriented to messaging, a BlackBerry forte, so the BlackBerry brand might be valued by one of its device makers (especially the BlackBerry Messenger brand for RIM's popular but proprietary mobile messaging service).
But users wouldn't get the physical keyboard associated with the BlackBerry brand. In neither case would IT get the security controls it associates with the BlackBerry moniker. The brand value seems more nostalgic than real, at least until people are given enough time to forget the original brand's specific attributes -- which may be why few old brands get resurrected for use on a different device.
The 500-strong security policies in BES
IT likes the BlackBerry because, when a BlackBerry Enterprise Server (BES) is also installed, IT can tie up the BlackBerry with an amazing variey of knots to control the device, how applications can interoperate, and what a user can do with it. For a control freak, a BES-managed BlackBerry is the ultimate playground. But IT is no longer calling the shots; if it were, RIM would be sitting pretty in the same spot it occupied in 2006, and iPhones and Androids would be at best interesting toys for 20-somethings. The truth is that for most use cases, IT has largely come to peace with the level of security in iOS and what is slowly emerging for Android.
There are of course some circumstances where BES's vast array of controls are actually necessary, and despite the capabilities of mobile device management (MDM) vendors, iPhones and Androids can't be managed to the required levels. I could imagine a defense contractor such as Harris or Computer Sciences Corp. (CSC) buying RIM to provision defense and spy clients, and the occasional other business, much as such firms today provisioned supersecure, hardened PCs to the same clientele.
Even here, you have to wonder about the long-term value of BES. Both the National Security Agency and Defense Dept. are working on more secure forks of Android, to get BlackBerry-like security while retaining the much more flexible capabilities of Android due to its support of a broad array of apps and services. Companies like Harris and CSC already see that writing on the wall, thus offering Android- and iOS-based systems for more broad military and government use.
Oh, and users don't buy BlackBerrys because they care about BES's policies. As users are now driving much of the mobile momentum, what matters to them will matter to RIM's fate and to any possible buyer. RIM knows that, as evidenced by its two years of talk about refocusing the BlackBerry for consumers, but its current OS and device lineup doesn't really walk that talk, despite the success of its popular BlackBerry Messenger instant messaging app.
The secure BlackBerry network
You don't hear much about this aspect of RIM's offering much these days, but it matters very much to security-conscious IT folks. RIM routes all messages through its servers, creating a secure connection to the enterprise servers that make it very difficult for a hacker to spoof their way in via a BlackBerry.
It's true that the cellular carriers pay a lot of attention to their own 3G and 4G networks' security, which may explain why network security is no longer a top selling point of the BlackBerry, but having that secure control in the middle remains a unique BlackBerry capability unmatched by iOS, Android, or Windows Phone. This use of the RIM network as a trusted middleman is also why some BlackBerry features don't work if you have only a Wi-Fi connection, as Wi-Fi communications don't go through the RIM server.