I was just starting to understand the question... when my comprehension disappeared in a cloud of silicon.
"I understand the idea of feeding a +ve current to a pin and to use a switch to turn the current off to activate a routine."
- just as jglenn alludes to.
Hold(force) the (input) pin high by connecting a resistor (10K, 50K, 100K whatever) to the positive supply. Then connect your switch from the same pin down to 0V.
So, if it were a push-button:-
1) Button released, input pin High.
2) Button pressed, input pin Ground.
This can then be 'sensed' in YOUR programme code as a 'button press'.
"My question is, can I keep a pin in the 'high' position without feeding a current and feed a negative signal to the same pin via switch to turn the signal off?"
- nearly the same question innit.
If you connect a resistor as described above to an input pin there will be very little current flowing. It would get the anoraks rustling to claim "without feeding a current", but the current would be mugger-all.
Please don't start using 'signal' as a phrase as it WILL confuse between voltages and currents.
When saying "feed a negative signal..." do you mean just connecting that same pin to Ground (usually the -ve battery terminal)?
If so then yes, like a push-button switch?
BUT WAIT, this is where the clouds of confusion come over and rain on my fireworks.
Are you now suggesting setting the pin HIGH in code and then use a push-button to ground it, in the vain hope of sensing it?
Don't. That could end up in an early bath and require your parents to shell out on a new PICAXE.
"I will probably build a circuit to test"
Well, er..um...yes.. ultimately there is no better way, BUT FIRST I would SUGGEST drawing your proposed circuit and posting it here. You sound like a novice and so may be getting it confused (I know I am).
And then just (in English) make a list of what you want your code to do.
Forget accurate sysntax for now (unless your BASIC is ok).