This one thing happened to my wife whilst out driving our last BX the Meteor, she had just pulled into our local medical centre when she heard a loud crash and then a horrible scraping noise (the exhaust falling down and scraping along the car park) after this she had a total lack of confidence in the car and hated driving it - we eventually sold it.
This appears to be a common rust spot for BX's as all the elements seem to find it and accumulate there, first thing I checked when I bought my BX19RD, solid as a rock this one.
We ended up having to have the whole corner rebuilt as the welding guy had to go back so far to get good metal it was unreal - luckily he was a mate and it only cost me £20 - the steel alone must have cost half that, let alone his labour to grind it all out and weld the new section in. After the carpets were put back and a good coat of underseal, you could hardly make out anything had been done, especially after a couple of months of road dirt had 'colour-toned' the new work in with the old.
I will now keep an eye on this one section as that little support stud is responsible for the whole rear end of the exhaust - from memory I can remember using a long length of garden wire wrapped round the towing eye to hold the exhaust up in order to get the missus home......
Not nice - hope you get it sorted.

Previous owner of a 1988 BX19 RD & Previous BX Meteor & Xantia Owner.
1995 Toyota Estima Lucida X Diesel