How tires fail
Every wheel on a car has two numbers in the mechanics window (press E near the car, or right-click and choose Vehicle Mechanics): condition and pressure. Condition drops with distance driven, with off-road driving and with crashes. Pressure is the air in the tire, and you set it with a Tire Pump.
A tire at 0% condition is finished. It cannot be patched back into service, so the only fix is to take it off and fit another. A car with a missing or ruined wheel will barely move and pulls hard to one side, which is the usual way players notice a flat in the first place.
Build 42 changed how air behaves. Player reports from early Build 42 say tires now lose pressure while you drive, where in Build 41 the value stayed put, so the pump matters more than it used to. Players also report that a wheel can come off when pressure or condition gets very low. They disagree on the exact cutoffs: one reply put the risk below 25 pressure, another corrected it to below about 5 pressure or 15% condition. Treat both as rough guides and keep your tires topped up.
