A car will normally start burning oil after so many miles.
When a car gets older and racks up the miles then the valve guides, seals and piston rings begin to get worn out and degrade.
The valve seals and valve guides that are worn out then allow the engine oil past them which then causes the engine oil to get into the exhaust and be burned with the fuel.
Engine oil can also leak past the piston rings and get into the engines cylinders which then gets burn with the fuel as well.
Or you could have an oil leaking out the rear seal or even oil pan gasket which could be where the oil is going as well.
But if it's just burning the oil then usually nothing bad will happen to the engine as long as you top up the engine oil often to prevent the engine from losing engine oil.
If an engine is burning oil then it means that the engine needs to be rebuilt and have all new valve seals, guides, piston rings etc installed into the engine for it to stop burning the engine oil.
You can usually rebuild an engine for the cost of the parts which is around $500.00 and some time if you know what you're doing.
I've rebuilt a few engines myself during winter months when there was nothing else to do and it was a fun experience and a good learning experience as well.
You can also just buy a replacement engine or have someone rebuild your engine for you for around $1,000.00 to $2,000.00 depending on the vehicle and how much work is involved.
Sometimes it's best to just get a new vehicle or different vehicle if the cost is too much.
I've driven many cars in my youth for many miles to and from work with the engine burning oil and those cars were still running when I finally parted them out.