I rarely grow invasive or potentially invasive vines in the ground and if i do, it's always in a place where I can control it and surrounded by inhospitable barriers. I remember one year someone sent me some Sweet Autumn Clematis - had no idea of it's growth habits .. when I discovered how invasive it was I Immediately tore it all out of the bed where I had it and put it all in triple plastic leaf bags. The following year I discovered it growing and flowering in an area where I used to dump my grass clippings .. I'm thinking the lawn mower must have run over a piece of it. It took all Summer to get all of it .. at least I thought I had gotten all of it - the following year I saw it again even though I had dug up the main root - at least I though I had .. the following year it showed up again and I went through the whole routine of digging it up. That was last year and I haven't seen it around this year .. keeping my fingers crossed. As pretty as it is, that stuff is like Kudzu - at least for my area.
I went through something similar with Honey Suckle - I knew it was invasive but did not realize how many seed it could produce in one season. After spending at least 15 minutes almost every day cutting off seed pods (there were 5 plants growing on posts) .. I cut it all down to the ground and (discovered there was no way I could dig out the roots), triple bagged it and put black buckets with bricks on the top over the main stems of the plants. It took 4 years for those to finally die - these plants managed to survive for years without light!
Having said that, some Passiflora can be extremely invasive and once they take hold, pretty much impossible to get rid of and oddly enough, pieces that break off will root in a heartbeat under the right conditions.
