Default [Q] Call connects on other end, but still rings on my end??

I'm not really sure if this is an isolated incident to a specific person or not.. but here is the situation:

I dial a number and my phone rings and rings and rings.. Eventually I hang up as there is no connection or voicemail. However, the other person picks up on their end and can hear EVERYTHING unbeknownst to me.

Am I alone on this or has anyone told you they can hear you even if the phone doesn't connect? This happened at least twice that I know of (just now and yesterday).