The distance or how far you can drive with a bad pulley depends on what type of pulley it is and how bad the pulley is.
If the pulley is an idler or tension pulley for the serpentine belt and it's squealing then it's a sign that the bearings are going out and you may be able to drive a few miles or sometimes farther before it seizes up and shreds your serpentine belt.
If the pulley is a bad crankshaft pulley and it's bent or coming loose then you should not drive the vehicle until the issue is fixed.
And if it's a power steering pump pulley or alternator or water pump pulley you can often drive a few miles or so until it eventually either comes off the shaft or shreds the belt.
You can drive with a loose pulley but you shouldn't drive the vehicle long as the pulley could eventually come even looser and the belt can slip off and may even cause the engine to overheat or cause you to lose power steering and your alternator power.
If the pulley is just slightly loose then you can drive a short distance but you should get the loose pulley fixed before driving too far as it could leave you stranded.
A loose pulley could cause overheating of the engine, especially if the loose pulley is causing the belt to slip on the water pump pulley and prevents the water pump from spinning as it should to effectively pump the coolant through the engine.
Loose pulleys that cause the serpentine belt or other belts to slip and prevent the belt from being tight around the water pump pulley can lead to the engine overheating.
Loose pulleys can eventually cause other failure of other pulleys and the belt or belts and could lead to damage to the engine if it overheats.
Some pulleys such as the water pump pulley, alternator pulley, power steering pump pulley, belt tension pulley, belt idler pulley should spin freely when the belt is off.
But other pulleys such as the crankshaft pulley should not spin freely and should have some resistance to turning.
The crankshaft pulley should not turn freely or spin freely by hand when the engine is off.
The crankshaft pulley should be able to rotate but should also be difficult to turn, especially by hand.
You should be able to use a socket and ratchet to turn the crankshaft pulley and it the crankshaft pulley does not rotate at all then there's an issue with the engine.
If the crankshaft pulley rotates freely then there's an issue with the engine.
The crankshaft pulley is connected to the crankshaft which also drives the pistons and rods in the engine and so it should be difficult to turn.
The crankshaft pulley also drives other engine components such as the power steering pump, alternator and water pump through the serpentine belt.
When the engine is running, the crankshaft pulley also rotates and this same rotation is transferred to these other accessories.
The crankshaft pulley should spin easily when the engine is running but not when the engine is off.
If the crankshaft pulley cannot be turned very easily or at all it could mean the engine is seized or something is locked up in the engine or the pulley is misaligned or there are worn components.
Other pulleys such as the water pump pulley, alternator pulley, and power steering pump pulley as well as idler and tension pulleys should be able to turn freely when the belt is not in place.