Is this NPN with base grounded and collector at negative voltage functional?
It is possible that the circuit is just drawn wrong. Is a mistake. But more likely, this is an example of a transistor being operated in the reverse active mode. In reverse active mode, the collector and emitter are basically swapped. Compared to forward active mode, reverse active mode has much lower beta and usually is considered to be not very useful.

Legends circulate that in the old days, BJT's might be used in reverse mode as switches. The saturation voltage (Vec) could be as low as a few mV, which could be useful for voltage sensing or other analog applications.

See also:
BJT in Reverse Active Mode of Operation