Assuming an open base, how low can Vce go (negative) before the transistor is damaged? Can I protect a transistor by connecting a diode's cathode to the collector and and anode to the Emitter?
If this is different depending on the transistor please use this one as an example http://www.nxp.com/documents/data_sheet/PBSS4350SPN.pdf
When the collector of an NPN transistor is negative with respect to the emitter, the C-B junction is forward biased, so you're essentially applying a reverse voltage to the B-E junction. According to the datasheet, the maximum that this transistor can withstand is 5V (VEBO). For any voltage greater than this, you'll need to limit the current externally in order avoid damaging the transistor.
Yes, you can connect a diode across the transistor to bypass reverse current around it, limiting the reverse voltage that the transistor sees to the VF of the diode.
This is directly answered in the datasheet right where you'd expect to find it:
The first two lines show you the maximum normal forward voltage the transistor can withstand. Usually, the backwards voltage is considerably less, which is also the case here. While the NPN transistor can withstand 50 V collector to emitter, it can only take 5 V accross reverse bias accross the base/emitter junction. Since applying a reverse voltage from emitter to collector would forward bias the base/collector junction, the base/emitter junction is the limiting factor.
So your answer is 5 volts, plus the B-C junction drop if you want to split hairs (which is not a good idea).
Yes, you could protect this transistor with a reverse diode accross the emitter/collector to clip reverse voltages to safe levels.
