This doesn't make any sense -- paying down debt instead of SPENDING the money increases net worth and is ultimately the same as socking money into a savings account if you're debt-free.
If your car dies and you can't get to work you can use your savings to fix your car so you can keep earning money.
Paying down your debt MAY increase the likelihood that you can borrow again. In the long term not paying interest on it will increase your income over time certainly but in the short term decreased debt and increased savings aren't interchangeable.
If they are truly strapped for cash because their house burned down but they don't have insurance they can still try to do without expensive vacations and other non obligatory expenses. If you can afford to keep paying $60k a year for 30 years for something that does no longer exist then there is no short term risk that is meaningfully destructive to your life.
Not if they pay for the car repair with debt, i.e. with a credit card. Not saying this is a good idea, but it makes more sense to pay down existing CC debt than to put money into a 2% savings account in case your car breaks down..
Paying down your debt MAY increase the likelihood that you can borrow again. In the long term not paying interest on it will increase your income over time certainly but in the short term decreased debt and increased savings aren't interchangeable.