Please explain why this simple circuit is latching 'on', but only when a fan is attached
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Your circuit.

A search for LFN shows up the PIC-1018SCL via this site. It's an infra-red receiver with built-in logic to pull its output low when IR is received.

In normal operation it will draw current from the base of Q1 via R1 when an IR signal is received. This will pass current to the motor and start it up. If all is well removing the IR source will result in the transistor switching off and the motor slowing to a stop.

The fact that it keeps going is a slight mystery as the LFN should be either fully off or on.

One possibility is that C1 is leaking a little current. If so, this will turn on the Q1 a little but not enough to supply the stall current and start up the motor. 

If, however, LFN pulls low, Q1 turns fully on and the motor spins up to speed, the current caused by leakage may be enough to keep the motor running.

Try removing C1 and see if you get the same effect.