England, I can tell you about, specifically in 1790-1829.

As usual "it depends" - on if "impoverished" means "insufficient funds" or "stony broke," what "do about" means, and the personality and morals of the people involved.

The rational choice, we would think, is a virtuous cutting back of expenses. Stop throwing expensive parties, stop gambling, lose the expensive mistress, sell the best horses. Many did sell off the non-entailed parts of their estates.

Earning money was trickier. One might use one's connections to get a government position. Many were sinecures, money for nothing. Many paid well enough that the person could afford to hire some clerk to move to Barbados and do the actual work in, say, customs, while the appointee stayed home in England. One might get a position involving light work, like being a private secretary (a man's job), or congenial work in politics. For younger men, buying a commission in the army was a possibility. Joining the Royal Navy was generally done early, if at all, as with Jane Austen's brothers or Lord Camelford. Lord Stonybroke couldn't decide to do it at thirty just to scrape an income.

There was enough of the old warrior nobility caste that going into trade or banking was frowned upon. Severely. Oddly, the sons of top bankers were welcomed in high circles, like "Apollo" Raikes, but they weren't noblemen descending (and the head of the Bank of England isn't just any banker).

Too many tried to recoup their fortunes thru the socially acceptable path of gambling. Honest trade = bad; gambling = good. This is what brought down "Beau" Brummell.

The ultimate retrenchment was to leave England and live abroad, because England was one of the more expensive places in Europe to live. Take Lady Hester Stanhope. When her uncle, the PM Pitt, died in 1806, she was no longer his hostess, no longer had a home, and only a pittance for income (a mere £1200 per annum). She tried hanging on in London, but her years of abusing her position came home to roost. She retired to Wales for awhile, but eventually travelled to the Mediterranean and settled outside Sidon. She managed to run up debts there that ate up her pension and lived in penury, helped by the charity of various ambassadors, residents, and a few old friends.

When all else had failed them, suicide was the last resort to cut short the pangs of starving to death.

I can remark on impecunious emigres in England, though not French customs. Some were supported by wealthy friends. Others became tutors, dancing masters, or successful coal merchants. Some made advantageous marriages. Some made marriages that kept them fed.