。
She had hardly any money.
Literal
She [topic-は] hardly money [object-を] was-not-holding.
持っている is the resultative state of 持つ ('to hold, carry, own') — Japanese marks 'have/possess' as a continuing state of holding. The negative past 持っていなかった means 'was not in a state of possessing' — i.e., 'didn't have.' ほとんど before the negative pulls it to 'hardly any.' This is the standard everyday way to say 'almost broke' in narration.