One thing they can specialize in
There is one thing they can continue to specialize in -- phones with keyboards!
I mean, really, I looked recently to see what phones with keyboard I could get, I've got a Stratosphere II (Android 4.1 phone with LTE). After I found VZW's website doesn't have a choice to filter by keyboard any more, I did some Googling. A review that went over the "top 10" on all 4 of the biggest US carriers had a BlackBerry Priv (which does look nice, it's running Android rather than BlackBerry 10), another BlackBerry, a 3rd BlackBerry, like 1 other Android (with a 640x480 screen and Android 4.0..., lower spec than the Strat II...) and a couple "feature phones" (calls, text, and pictures only.)
Some people now have the solution of having a phone, tablet, or "phablet" and a plug-in keyboard. That's fine, but I don't want to have to carry around accessories with my phone.
Blackberry should think about this -- it's unfortunate that the BlackBerry itself (i.e. a phone running BlackBerry OS) has become niche. But the "Android phone with keyboard" alone is a distinguishing feature for them; they could make a flaghsip phone (as they are now), mid-range, or low-end and not have to worry about it being "yet another Android phone" and not stand out.
If there's enough current BlackBerry OS users too, it would make sense to keep getting customers from that niche too, they could make sure BB runs on the same hardware and get 2 for one.