Step 1: Break down the target meaning: 'a person who is unable to pay their debts' relates specifically to money and financial obligations.
Step 2: Analyse the options by their roots. 'Indolent' relates to laziness, not finance. 'Ineligible' means not qualified for something, unrelated to debt. 'Incompetent' means lacking skill or ability in a task, also unrelated to finance specifically.
Step 3: 'Insolvent' breaks down as the prefix 'in-' (not) plus 'solvent', from the Latin 'solvere' (to loosen, release, or pay off). A solvent person can pay their debts; an insolvent person cannot, which precisely matches the definition given.
Correct option: (4) Insolvent.