If a pulley is loose it will eventually come off the shaft and can also cause belt slippage and other issues and even could possibly shred the belt.
A pulley that is loose should be tightened up immediately to prevent any possible further damage or problems as it will eventually come off the shaft.
To prevent pulley slippage ensure that the pulley is aligned properly and the the belt is the right size and is tightened properly or if the belt has a tensioner ensure the belts tensioner is in good shape and maintaining the tension of the belt.
Also be sure the pulley is clean and ensure that you have the belt in any grooves of the pulley properly.
If your pulley belt keeps coming off it could be that the belt is too large or not tight enough or the pulley could be misaligned as well.
To fix a misaligned pulley you will need to adjust the position of the pulley to align the pulley with the other pulleys and the belt's path.
You will need to loosen the pulley's mount and move the pulley into the correct position and then re tighten the mount.
Some pulleys use a bolt to hold the pulley onto the shaft and if that is the case you will need to loosen the bolt which sometimes takes an Allen wrench.
Then if the pulley has a key you should ensure the key is not warped or broke or missing and if so replace the pulley shaft key and then align the pulley up on the shaft and re tighten the bolt that holds the pulley to the shaft.
If pulleys are not aligned properly it can cause the belt to slip of the pulley and even shred the belt.
To put a pulley back on a shaft, first ensure that the shaft is clean and free of any rough edges and if a key is needed on the shaft be sure to install the key on the shaft before sliding the pulley back on.
Some pulleys may easily slide onto the shaft and then if it has a bolt holding it onto the shaft you tighten the bolt until it's tight enough to hold the pulley on.
Some pulleys are also press fitted like with a power steering pump pulley.
If it's a power steering pump pulley you place the pulley over the power steering pump shaft and then use a power steering pump pulley installer and removal tool to push it back onto the shaft.
To prevent problems and the possibility of a power steering pump pulley coming off the shaft you should always use a new pulley as they are pressed fit and designed to fit tight.
You cannot hammer on a pulley especially when the pulley is on a shaft of a motor, power steering pump or other pump or shaft which could be damaged.
Hammering on a pulley can cause damage to the pulley and shaft and motor or pump that the pulley is being installed on.
For proper pulley installation it's best to use a special tool like a pulley installer and remover.
These tools are designed to both pull a pulley off it's shaft safely and also push the pulley back onto it's shaft.
Never hammer on a pulley that is going onto an electric motor or other pump including a power steering pump as it can and will result in damage to the motor, pump and even the pulley.
For power steering pump pulleys the pulley should fit tightly on the shaft and be pressed on with a power steering pulley tool.
The power steering pump pulley should also be pulled off using the same tool without any hammering.
Pulley remover tools and pulley installer tools are not all that expensive and also make the job much easier and faster.
If you're installing a pulley such as on a mower engine or electric motor you can safely gently tap it onto the shaft with a hammer if need be but don't full on hammer it as it can lead to damage.