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wedrifid comments on When is it ever rational to enter a sweepstakes where you may have a 1/10,000 chance of winning? - Less Wrong Discussion
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When you are desperate. ie. You owe money to a loan shark and will do anything to reduce the chance of having your kneecaps busted.
Even in other debtor situations where you face a set penalty, like (non-violent) bankruptcy, for falling $X short and $(X-1) dollars short, it can be rational to spend money to enter sweepstakes.
It can in theory, though it is worth remembering that in practice it is vastly more likely that you are better off to forget about long shots, grit your teeth and focus on putting together a realistic proposal for paying off the debt in installments.
It's not just about sweepstakes being a long shot - being in debt is a very tough test of rationality, because you have a terribly strong incentive to say what your creditors want to hear, combined with a death spiral of learned helplessness. It's the one time when you can't afford any emotional distractions.
On the bright side, if you can get enough of a grip on reality to navigate your way out of that situation, tougher tests than that will be few and far between.