The pair were speaking at the Off The Ball Roadshow last night
Connacht can secure a home Pro12 semi-final this weekend with victory over Glasgow Warriors and continue their search for a maiden competition crown.
The unprecedented success they have enjoyed this season has been exemplary of the spirit and quality Pat Lam's side have shown all season. But this, of course, wasn't always the case.
Speaking on last night's Off The Ball Roadshow in Galway, former player Gavin Duffy and journalist John Fallon explained how close the club had come to going under.
"Into my second season with Connacht there was talk of Connacht being disbanded," said Duffy, "There had been financial difficulties in the IRFU and one of the options was to get rid of Connacht.
"It only really hit us when Eric Elwood (assistant coach) came back from a meeting he had attended in Dublin and came back in with Dan McFarland (former forwards coach) and they explained how grave the situation was.
"Eric was in tears, Dan was in tears and Dan had only been with the club for three years at that stage. That's really when it hit us that wow this could actually be happening. IRUP had just been established at this stage, Liam Toland was driving that. All of a sudden we were all very interested in IRUPA whereas before the attitude was that we didn't really need it.
"As players we figured we had to keep winning matches so they'd have no reason to get rid of us, but it appeared it wasn't going to be enough at the time. There was a lot of political stuff going on in the background."
John Fallon, head coach at Connacht back in 2002, said that it didn't take long after his appointment for things to become worrying.
"Within a couple of months of my appointment, that's when the whole thing emerged that Connacht might be disbanded.
"If you think back on it, professional rugby was only six years old at that time. There wasn't a template and in fairness to the IRFU there was nothing they could follow anywhere else in the world. People were feeling their way around in the dark."
It took supporters to march on the IRFU to affect change and help the club to survive. You can listen to the full story below.