Is there a biological neuron that spikes in response to hyperpolarizing currents?
I was doing some more research and stumbled upon this paper here by Dr. Izhikevich that describe neurons as a system that can exhibit resonance. The author built a model that he calls the resonate and fire, which is a linear piece-wise model of a neuron. 

The interesting thing, and why I bring it up, is it can respond to a "two inhibitory pulses, that if timed correctly will cause the neuron to fire. but neither inhibitory pulse alone can cause the neuron to fire. 

Following some of the citations in the article (found here), apparently thalumus neurons can exhibit resonance and thus theoretically can fire in response to the right frequency of input. However it is important to note that they thalamic neurons are close to threshold, and are not receiving the double inhibitory input that Izhekivich talks about in his paper. The second paper uses a ZAP protocol. 

A Zap protocol is injecting a Sine wave into a neuron and slowly change the frequency linearly in time. 

$$I_{ZAP}(t) = \sin((\omega_0+\omega t) t) $$ where $\omega_0$ and $\omega_1$ are constants.