True & Honest Fan
If they are legitimately cut off, it often is in the works before they troon out, because trooning out is the manifestation of mental illnesses rather than the cause of them. Equally as often, as you said, they cut their family off for not 'being supportive enough' (nearly always in the form of money), and then claim it's the other way around because troons are only victims, never perpetrators.Very informative post about "Elena." As for your question, my best bet is that they were cut off from or renounced the family wealth the moment they trooned out. That would allow them to claim oppression points for both being transgendered and having no money, allowing them to get the position with TLL.
And some of the time, they just lie, and while they likely trash their family to everyone they know, they still have enough of a relationship with them to be have at the very least a safety net for when they really fuck up.
tl;dr: Never trust a troon.